Solving Word Problems, Geometry, Percents, Mixtures
Set up the equation but do not solve:
1. A number plus 3 times the number is twice the number less six.
n + 3n = 2n - 6
2. The quotient of a number and the number plus 4 is twice the number.
n/(n+4) = 2n
Solve the following:
3. Jim sells homes and earns a 4% commission on all he sells. If he made a commission of $1900 on
one home he sold, what was the total price of the house?
1900 = 4% (x)
1900/0.04 = 190000/4 = $47,500
4. Simon invested $2600 in a simple interest account for two years. If the account yielded $234,
what was the interest rate? Writ your answer as a percent.
234 = n% (2600)
234/2600 = 117/1300=0.09, 9%
5. Julie wants to buy an I-phone that costs $120 before tax. If she lives in an area with a 9.25%
sale-tax, what will be the total I-Phone price, with tax included?
Tax = 0.0925*120 =11.10
Cost = 120 + 11.10 = $131.10
6. A bicycle that sells for $350 is 25% off. What will the sales price be?
Discount = 0.25 * 350 = $87.5
Price = 350 – 87.5 = $262.50
7. The measure of one angle of a triangle is twice the second and ten degrees more than three
times the third. What are the three angles? (Hint: the angles add to 180 degrees)
angle1 = 2(angle2) or angle 2 = ½ angle1
angle1 = 10 + 3 angle3 or angle 3 = (angle1 – 10)/3
If angle1 = x, angle2 = x/2, angle3 = (x-10)/3
x + x/2 + (x-10)/3 = 180, Multiply by 6, 6x + 3x + 2x – 20 = 1080, 11x = 1080 +20 = 1100
11x=1100, x = 100, angle 1 = 100, 100 = 2(angle 2), angle 2 = 50, 100 = 10 + 3(angle 3),
angle 3 = 90/3 = 30 deg
Angles are 100, 50, and 30 degrees
8. The width of a rectangle is one half its length, less 2 inches. If the perimeter of the rectangle is
35 inches, what are the length and width?
W = L/2 - 2
P =2W + 2L = 2(L/2 – 2) + 2L = L – 1 +2L= 3L-1 = 35
3L = 36
L = 12 in, W = 6-4 = 4 in
9. A school has 45% girls. If the kindergarten class has 15 girls and 20 boys, does it have the same
ratio of boys and girls as does the school? If not, does is the ratio larger or smaller?
45/100 compared to 15/20
45/100 = 9/20, so the kindergarten has a larger ratio of girls to boys
10. Joe receives and inheritance of $50,000 from his uncle. He invests part of his money in the stock
market, earning a return of 6% and part in a savings account with a return of 2%. At the end of
the year, he has earned $2500. How much did he invest in stocks and how much in savings?
This is a mixture problem
Account Amount
Rate
Earnings
Stocks
x
6%
0.06x
Savings 50,000-x
2%
0.02 (50,000-x)
Total
50,000
0.06x + 0.02(50,000-x) = 2500
0.06x - 0.02x + 1000 = 2500
0.04x = 1500, x = 150000/4 = 37,500; 37,500 in stocks, 12,500 in savings