The Division and Multiplication Properties of Equality
buttons.Translate and Solve Applications
To solve applications using the Division and Multiplication Properties of Equality, we will follow the same steps we used in the last section. We will restate the problem in just one sentence, assign a variable, and then translate the sentence into an equation to solve.
Example 2.25
Denae bought 6 pounds of grapes for $10.74. What was the cost of one pound of grapes?
Solution
| What are you asked to find? | The cost of 1 pound of grapes |
| Assign a variable. | Let c = the cost of one pound. |
| Write a sentence that gives the information to find it. | The cost of 6 pounds is $10.74. |
| Translate into an equation. | \(6c=10.74\) |
| Solve. |
\(\frac{6c}{6}=\frac{10.74}{6}\) \(c=1.79\) |
| The grapes cost $1.79 per pound. | |
|
Check: If one pound costs $1.79, do 6 pounds cost #10.74? \(6(1.79) \stackrel {?} {=} 10.74 \) \(10.74=10.74\) ✓ |
Table 2.3
Try It 2.49
Translate and solve:
Arianna bought a 24-pack of water bottles for $9.36. What was the cost of one water bottle?
Try It 2.50
Translate and solve:
At JB's Bowling Alley, 6 people can play on one lane for $34.98. What is the cost for each person?
Example 2.26
Andreas bought a used car for $12,000. Because the car was 4-years old, its price was \(\frac{3}{4}\) of the original price, when the car was new. What was the original price of the car?
Solution
| What are you asked to find? |
The original price of the car |
| Assign a variable. |
Let \(p\) = the original price. |
| Write a sentence that gives the information to find it. |
$12,000 is \(\frac{3}{4}\) of the original price. |
| Translate into an equation. |
\(12,000=\frac{3}{4}p\) |
| Solve. |
\(\frac{4}{3}(12,000)=\frac{4}{3}·\frac{3}{4}p\) \(16,000=p\) |
| The original cost of the car was $16,000. | |
| Check: Is \(\frac{3}{4}\) of $16,000 equal to $12,000? \(\frac{3}{4} · 16,000 \stackrel {?} {=} 12,000 \) \(12,000=12,000\) ✓ |
Table 2.4
Try It 2.51
Translate and solve:
The annual property tax on the Mehta's house is $1,800, calculated as \(\frac{15}{1,000}\) of the assessed value of the house. What is the assessed value of the Mehta's house?
Try It 2.52
Translate and solve:
Stella planted 14 flats of flowers in \(\frac{2}{3}\) of her garden. How many flats of flowers would she need to fill the whole garden?