Question

equations in real - world situations

1. match each situation with the equation that best represents the situation.

situation
equation
a. there are 15 dogs at a shelter. the number of dogs is 5 times the number of cats. let x represent the number of cats.
15 = x - 5
b. there are 15 fish at a pet store. the number of fish is 5 more than the number of hamsters. let x represent the number of hamsters.
5 = 15x
c. there are 5 birds at a pet store. the number of mice is 15 more than the number of birds. let x represent the number of mice.
15 = 5x
d. a bowl has 5 cups of cat food. 15 cats share the food equally. let x represent the number of cups of cat food each cat receives.
15 = x + 5

1. let w represent the width of a rectangle in inches. let l represent the length of the rectangle in inches. the formula p = 2w + 2l represents the perimeter of the rectangle. what is the perimeter of a rectangle that has a width of 8.5 inches and a length of 13 inches?
2. sana and her family go on a road trip. sana uses the equation $s = \frac{250}{t}$, when $t > 0$, to determine s, the car’s speed in miles per hour when the family drives for t hours. she determines that the car’s speed when the family drives for 4 hours is 65 miles per hour. is sana correct? explain.

Explanation:

Question 9

Match each situation to the equation by translating the verbal description to a mathematical expression.

Step1: Substitute given values

$w=8.5$, $l=13$ into $P=2w+2l$
$P=2(8.5)+2(13)$

Step2: Calculate each term

$2(8.5)=17$, $2(13)=26$

Step3: Sum the terms

$P=17+26$

Step1: Substitute $t=4$ into formula

$s=\frac{250}{4}$

Step2: Compute the speed

$s=62.5$

Step3: Compare to Sana's value

$62.5
eq 65$

Answer:

a. $15=5x$
b. $15=x+5$
c. $15=x-5$
d. $5=15x$

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Question 10