Unit 3: Writing Equations
Lesson 3: Standard Form Real World Problems
When you write an equation in standard form, you should read the problem and look for:
•
•
Information about 2 different things that when added together will give you a total.
A total
Example 1
Jamie is planning a dinner party. Chicken entrees cost $15 per head and fish entrees cost $18
per head. Jamie has a budget of $225 for the dinner party.
•
•
Write an equation that represents Jamie’s situation.
If five people request fish entrees, how many chicken entrees can she buy?
Copyright© 2009 Algebra-class.com
Unit 3: Writing Equations
Word Problems Organizer
What I Know
Define Your Variable(s).
Write a Verbal Model & Substitute
Solve
Solution
Copyright© 2009 Algebra-class.com
Unit 3: Writing Equations
Lesson 3: Real World Problems & Standard Form
1. At your local market, ground beef costs $2 per pound and chicken breasts cost $3 per
pound. You have a total of $30 to spend on ground beef and chicken for a party. Which
equation represents the amounts of ground beef and chicken you can buy?
Let x represent the number of pounds of ground beef and y represent the number of pounds
of chicken breasts.
A. 3x +2y = 30
B. 2x +3y = 30
C. y = 2x +3
D. 30x +3y = 2
2. Use the equation from problem 1 above to solve:
If you buy 3 pounds of ground beef, how many pounds of chicken can you buy for $30?
A. 8 pounds of chicken
B. 10.5 pounds of chicken
C. 18.5 pounds of chicken
D. None of the above.
Copyright© 2009 Algebra-class.com
Unit 3: Writing Equations
3. You are in the running to be elected a member of your town council You have $275 to
spend on advertising. It costs $2 to make a button and $1.50 to make a sign.
• Write an equation that represents the different number of buttons, x, and signs, y you
could make.
• If you make 50 buttons, how many signs can you make?
4. Jessica made 240 oz of jam. She has two types of jars. The first holds 10 oz and the
second holds 12 oz.
• Write an equation that represents the different numbers of 10 oz jars, x, and 12 oz jars,
y, that will hold all of the jam.
• If Jessica used 16, 10 oz jars, how many 12 oz jars would she be able to make?
Your next assignment will be a quiz. You will need to know:
•
How to write an equation in slope intercept form and how to write an equation in standard form.
Copyright© 2009 Algebra-class.com
Unit 3: Writing Equations
1. You are purchasing “photo books” as holiday gifts this year. A 5 page
photo book costs $10.50 and a 10 page photo book costs $17.50. You
have a total of $217 to spend on holiday gifts.(4 points)
•
•
•
Write an equation that you could use to determine how many 5 page photo books (x) you
could purchase and how many 10 page photo books (y) you can purchase.
If you decide that you need four 5 page photo books, how many ten page photo books can
you purchase?
Justify your answer mathematically.
2. A youth group is purchasing tickets to a local amusement park. Adult tickets cost $15.50 and
child tickets cost $10.25. They have a total of $545 to spend on tickets. (4 points)
•
•
•
Write an equation that the youth group could use to determine the total number of adult
tickets (a) and the total number of child tickets (c) that they can purchase.
They have 32 children going to the amusement park. How many adult tickets can they buy
as chaperones?
Justify your answer mathematically.
Copyright© 2009 Algebra-class.com
Unit 3: Writing Equations
Lesson 3 - Real World Problems & Standard Form – Answer Key
1. At your local market, ground beef costs $2 per pound and chicken breasts cost $3 per
pound. You have a total of $30 to spend on ground beef and chicken for a party. Which
equation represents the amounts of ground beef and chicken you can buy?
Let x represent the number of pounds of ground beef and y represent the number of pounds
of chicken breasts.
Ground Beef
+ Chicken
= Total Amount
A. 3x +2y = 30
Price • # of pounds + Price • # of pounds = Total Amount
B. 2x +3y = 30
2• x
+
3 • y
= 30
C. y = 2x +3
2x +3y = 30
D. 30x +3y = 2
2. Use the equation from problem 1 above to solve:
If you buy 3 pounds of ground beef, how many pounds of chicken can you buy for $30?
A. 8 pounds of chicken
2x +3y = 30
x = 3 (# of pounds of ground
beef)
C. 18.5 pounds of chicken
2(3) + 3y = 30
Substitute 3 for x
D. None of the above.
6 + 3y = 30
Simplify: 2(3) = 6
B. 10.5 pounds of chicken
Solve for Y:
6-6 +3y = 30 -6
Subtract 6 from both sides
3y = 24
Simplify: 30 – 6 = 24
3y = 24 = 8
3
3
You could buy 8 lbs of
chicken.
y=8
Copyright© 2009 Algebra-class.com
Unit 3: Writing Equations
3. You are in the running to be elected a member of your town council. You have $275 to
spend on advertising. It costs $2 to make a button and $1.50 to make a sign.
• Write an equation that represents the different number of buttons, x, and signs, y you
could make.
• If you make 50 buttons, how many signs can you make?
Advertising Costs:
Buttons
Signs
= Total
Price • # of buttons
+ Price • # of signs
= Total
2
+
• x
+
1.50 • y
= 275
2x +1.50y = 275
• 2x +1.50y = 275 is the equation that represents the different number of buttons and
signs you could make with $275.
Part 2: If you make 50 buttons, how many signs can you make?
If you know you have to make 50 buttons, then you know your value for x, the number
of buttons. Let’s substitute 50 for x and solve for y.
2x +1.50y = 275
2(50) + 1.50y = 275
Substitute 50 for x, the number of buttons.
100 +1.50y = 275
Simplify: 2(50) = 100
Solve for Y:
100 -100 +1.50y = 275-100
Subtract 100 from both sides.
1.50y = 175
Simplify: 275 - 100
1.50y = 175
1.50
1.50
Divide both sides by 1.50
• You could make 116 signs if you make 50 buttons.
Y = 116.6
*You can’t make .6 of a sign, and you can’t round up
because you would go over your limit of $275. Therefore, you must round down.
Copyright© 2009 Algebra-class.com
Unit 3: Writing Equations
4. Jessica made 240 oz. of jam. She has two types of jars. The first holds 10 oz. and the
second holds 12 oz.
• Write an equation that represents the different numbers of 10 oz jars, x, and 12 oz jars,
y, that will hold all of the jam.
• If Jessica used 16, 10 oz jars, how many 12 oz jars would she be able to make?
10 oz. jars
+ 12 oz. jars
= total number of oz.
10 oz• # of jars + 12oz. • # of jars = total number of oz.
10 •
x
+ 12
• y
= 240 oz
10x +12y = 240
• The equation that represents the different number of 10 oz jars and 12 oz jars that
will hold all of the jam is: 10x +12x = 240.
Part 2: If Jessica used 16, 10 oz. jars, how many 12 oz. jars would she be able to make?
The variable that represents 10 oz. jars is x, so let’s substitute 16 for x and solve for y.
10x +12y = 240
10(16) + 12y = 240
160 +12y = 240
Solve for y:
160 – 160 +12y = 240 – 160
12y = 80
Substitute 16 for x.
Simplify: 10(16) = 160
Subtract 160 from both sides
Simplify: 240 – 160 = 80
12y = 80
12
12
Divide by 12 on both sides
y = 6.67
Simplify: 80/12 = 6.67
• If Jessica used 16, 10 oz. jars, she could make 6, 12 oz. jars.
**y = 6.67 but you can’t really make .67 of a jar. You can’t round up because then you
would exceed 240 oz., so you must round down in this case.
Copyright© 2009 Algebra-class.com
Unit 3: Writing Equations
1. You are purchasing “photo books” as holiday gifts this year. A 5 page
photo book costs $10.50 and a 10 page photo book costs $17.50. You have
a total of $217 to spend on holiday gifts.(4 points)
•
Write an equation that you could use to determine how many 5 page photo books (x) you
could purchase and how many 10 page photo books (y) you can purchase.
Cost of 5 page·(# of 5 page) + Cost of 10 page·(# of 10 page) = Total
10.50x
+
17.50y
= 217
The equation that can be used to determine the total number of photo books that can be purchased is:
10.50x + 17.50y = 217
•
If you decide that you need four 5 page photo books, how many ten page photo books can
you purchase?
I know that I need four 5 page photo books, therefore, I can substitute 4 for x into the equation and solve for
y.
10.50(4) + 17.50y = 217
Substitute 4 for x.
42 + 17.50y =217
Simplify: 10.5(4) = 42
42 – 42 + 17.50y = 217-42
Subtract 42 from both sides
17.5y = 175
Simplify: 217-42 = 175
17.5y/17.5 = 175/17.5
Divide by 17.5 on both sides
Y = 10
Simplify: 175/17.5 = 10
If you buy 4, 5 page photo books, then you will be able to buy 10, 10 page photo books for $217.
•
Justify your answer mathematically.
In order to justify your answer mathematically, you must substitute for x and y to determine if the
equation is mathematically correct.
X=4
y = 10
10.5(4) + 17.5(10) = 217
42 + 175 = 217
217 = 217
Yes, my equation is correct!
Copyright© 2009 Algebra-class.com
Unit 3: Writing Equations
2. A youth group is purchasing tickets to a local amusement park. Adult tickets cost $15.50 and
child tickets cost $10.25. They have a total of $545 to spend on tickets. (4 points)
•
Write an equation that the youth group could use to determine the total number of adult
tickets (a) and the total number of child tickets (c) that they can purchase.
Price of adult(# of adult) + Price of child(# of child) = Total
15.50a
+
10.25c =
545
The equation that can be used to determine the total number of adult and child tickets is:
15.50a + 10.25c = 545
•
They have 32 children going to the amusement park. How many adult tickets can they buy
as chaperones?
Since I know that I have 32 children going, I can substitute 32 for c and solve for a.
15.50a + 10.25(32) = 545
Substitute 32 for c.
15.50a + 328 = 545
Simplify: 10.25(32) = 328
15.50a + 328 – 328 = 545 – 328
Subtract 328 from both sides
15.50a = 217
Simplify: 545 – 328 = 217
15.50a/15.50 = 217/15.50
Divide by 15.50 on both sides
a = 14
If they take 32 children to the amusement park, then they can take 14 adults as chaperones
for $545.
•
Justify your answer mathematically.
In order to justify mathematically, we must substitute for a and c to determine if the equation is
mathematically correct.
15.50a + 10.25c = 545
15.50(14) + 10.25(32) = 545
217 + 328 = 545
545 = 545
Yes! My equation is mathematically correct!
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