Solving Literal Equations
Ratios and Proportions
Similar figures and models
The Percent Equation
Percent Change and Error
Money
100
Solve the equation A = lw for w
W=4
100
Convert the ratio 66 feet/ second to miles per hour.
45 miles per hour
100
Triangle ABC is similar to Triangle DEF. If AB = 6, BC = 8, and DE = 9, find the length of side EF.
EF = 12
100
What number is 25% of 160?
40
100
Find the percent change from 50 to 65. State whether it is an increase or decrease.
30% increase
100
Calculate the simple interest earned on a principal of $1,200 at an annual interest rate of 4% for 3 years. (I = Prt)
$144
200
Solve the equation y = mx + b for x.
x = (y - b) / m
200
Solve the proportion: x / 15 = 4 / 5
x = 12
200
A flag pole casts a shadow that is 24 feet long. At the same time, a 6-foot-tall person casts a shadow that is 4 feet long. How tall is the flag pole?
36 feet
200
18 is what percent of 45?
40%
200
Find the percent change from 80 to 60. State whether it is an increase or decrease.
25% decrease
200
An item costs $45.00 and the sales tax rate is 7%. Find the total cost including tax.
$48.15
300
Solve the equation P = 2l + 2w for l.
l = (P - 2w) / 2
300
Solve the proportion: 3 / (y - 2) = 6 / 10.
y = 7
300
A scale model of a building has a scale of 1 inch = 12 feet. If the model is 7.5 inches tall, what is the actual height of the building?
90 feet
300
42 is 70% of what number?
60
300
An item's price increased from $40 to $46. What is the percent increase?
15% increase
300
A meal costs $32.00. You want to leave an 18% tip. How much tip should you leave?
$5.76
400
Solve the equation (2d+3)/5 = (3d-6)/8 for d.
d = -54
400
Solve the proportion: (x + 3) / 4 = (x - 1) / 2
x = 5
400
A map uses a scale of 2 cm = 15 km. If two cities are 9 cm apart on the map, what is the actual distance between them?
67.5 km
400
What number is 125% of 48?
60
400
You estimated that a room was 15 feet wide, but the actual width was 16 feet. Find the percent error to the nearest tenth of a percent.
6.25% error
400
Grandma has $250,000 to invest. She divides her money into two accounts. One account is ultra-safe treasury bills paying 4% interest, and the other is in the riskier corporate bonds paying 6%. If she needs $12,000 per year in income from her investments, how much should she invest in every year?
150k in treasury, 100k in corporate
500
Solve the equation 5= (2m-b)/(m+b) for m
m=-2b
500
A car travels 180 miles on 6 gallons of gas. How many miles can it travel on 11 gallons of gas?
330 miles
500
.
Find W
If the Front face of the smaller figure has an area of 80, what is the area of the corresponding face of the larger figure?
If the volume of the larger figure is 3000, what is the volume of the smaller figure?
a) w=4 b) 500 c) 192
500
A store offers a 15% discount on a jacket. If the discount amount is $18, what was the original price of the jacket?
$120
500
A scientist measures the mass of a sample to be 12.4 grams. The accepted actual mass is 12.5 grams. Calculate the percent error.
0.8% error
500
A pair of shoes costs $80. They are on sale for 20% off, and sales tax is 6% (applied to the sale price). What is the final total price?
$67.84 (Sale price: $64, Tax: $3.84)