Question

1. solve the proportions. show all work.

a. \\(\frac{35}{25} = \frac{15 - c}{5}\\)
b. a car uses 5 gallons of gasoline to travel 97.5 miles. at this rate, how many miles can the car travel using 13 gallons of gasoline?

Explanation:

Part a: Solve the proportion $\boldsymbol{\frac{35}{25} = \frac{15 - c}{5}}$

Step 1: Simplify the fraction

Simplify $\frac{35}{25}$ to $\frac{7}{5}$. So the equation becomes $\frac{7}{5}=\frac{15 - c}{5}$.

Step 2: Cross - multiply

Since the denominators are the same, we can set the numerators equal: $7 = 15 - c$.

Step 3: Solve for $c$

Subtract 15 from both sides: $7-15=15 - c-15$, which gives $- 8=-c$. Multiply both sides by - 1 to get $c = 8$.

Step 1: Find the miles per gallon (mpg)

The car uses 5 gallons to travel 97.5 miles. The miles per gallon is calculated by dividing the distance by the number of gallons. So, mpg $=\frac{97.5}{5}=19.5$ miles per gallon.

Step 2: Calculate the distance for 13 gallons

To find the distance traveled with 13 gallons, we multiply the miles per gallon by the number of gallons. So, distance $=19.5\times13 = 253.5$ miles.

Answer:

$c = 8$

Part b: Distance traveled with 13 gallons