5-A16
Linear Systems Word Problem Practice
Math 8H
ALL WORK IS TO BE SHOWN NEATLY IN YOUR COMPOSITION BOOK. BE SURE TO LABEL THE
VARIABLES AND WRITE AN ALGEBRAIC EQUATION OR SYSTEM OF EQUATIONS FOR EACH
PROBLEM. REMEMBER TO CHECK THAT YOU HAVE ANSWERED THE QUESTION THAT WAS ASKED!
1.
How many liters of water must be added to 50 L of a 30% acid solution in order to
produce a 20% acid solution?
2.
Students working at a refreshment stand mix cranberry juice at 50 cents per liter and
apple juice at 35 cents per liter to make 120 liters of a fruit drink worth 40 cents per
liter. How many liters of each did they use?
3.
The Esperanzas invested part of their $8000 at 12% and part at 8%. If their annual
investment income is $825, how much is invested at each rate?
4.
The sum of two numbers is 66. If the smaller number is subtracted from two-thirds of the
larger number, the result is one-third the positive difference of the original numbers. Find
the numbers.
5.
A square house is 24 ft. long, and the house is located on a lot that is 50 ft. longer than
it is wide. The perimeter of the lot is 20 ft. more than 5 times the perimeter of the house.
Find the length of the lot.
6.
In a math contest, each team is asked 50 questions. The teams earn 15 points for each
correct answer and lose 8 points for each incorrect answer. One team finished with a score
of 566. How many questions did this team answer correctly?
7.
A rowboat can travel a distance of 66 km in 3 hours with the current. The rowboat can
travel 33 km in 3 hours against the current. Find the rate (speed) of the current.
8.
How many liters of water must be evaporated from 10 L of a 40% salt solution to
produce a 50% solution?
9.
A plane averaged 1000 km per hour flying from LA to Casper, Wyoming, but heavy winds
slowed its speed on the return trip to 600 km per hour. If the entire trip took 6 hours of
flying time, find the distance from LA to Casper.
10.
A grocer mixes two types of nuts, Brand A and Brand B. If the mix includes 4 kg of
Brand A and 6 kg of Brand B, the mix will cost $6.20 per kilogram. If it includes 2 kg of
Brand A and 8 kg of Brand B, it will cost $5.60 per kilogram. Find the cost per kilogram
of each brand.
Key 5-A16 Handout
1. Let x = amt. of water added
Let y = amt. of final mix
50 + x = y
.30(50) + 0x = .20y
(% • amt. + % • amt. = % • amt.)
25 L of water.
2. Let C = amount of C juice
Let A = amount of A juice
C + A = 120
.50C + .35 A = (120)(.40)
(cost • amt. + cost • amt. = cost • amt.)
40 liters of C Juice, &
80 Liters of A Juice.
3. Let x = amount at 12%
Let y = amount at 8%
x + y = 8,000
12x + 8y = 82500
$4,625 at 12%, & $3,375 at 8%.
4. Let x = the smaller
Let y = the larger
x + y = 66
2
1
y – x = (y – x)
3
3
The numbers are 22 and 44.
5. L = W + 50
2W + 2L = 5(24 • 4) + 20
Length is 150 feet.
6. Let x = # correct
Let y = # incorrect
x + y = 50
15x – 8y = 566
42 questions correct.
7. Let b = boat’s speed
Let c = current’s speed
with  3(b + c) = 66
against  3(b – c) = 33
(time • rate = distance)
5
1
kmh is current speed.
2
8. Let x = amt. of water evap.
Let y = amt. of final mix
10 – x = y
.40(10) – 0x = .50y
(% • amt. + % • amt. = % • amt.)
2L
9. Let x = time there
Let y = time back
x+y=6
1000x = 600y
(dist. there = dist. back)
2,250 km
10.Let A = Cost per kg. of A
Let B = Cost per kg. of B
4A + 6B = 10(6.20)
2A + 8B = 10(5.60)
(wt. • cost + wt. • cost = wt. • cost)
$8 per/kg for A, & $5 per/kg for B.