Math  /  Algebra

QuestionTwo friends, Zachary and Nachelle, had just bought their first cars. Nachelle uses 13 gallons of gas to drive 196.3 miles in her car. The table below represents the number of miles, yy, that Zachary can drive his car for every xx gallons of gas.
Zachary's Gas Mileage Gallons (xx) | Miles (yy) ---|--- 3 | 87 5 | 145 7 | 203 9 | 261
Use the dropdown menu and answer-blank below to form a true statement.
Answer Attempt 1 out of 2
Nachelle's car gets \_\_\_\_\_\_ miles per gallon \_\_\_\_\_\_ than Zachary's car.

Studdy Solution

STEP 1

What is this asking? We need to figure out how many miles per gallon each friend gets, and then compare them. Watch out! Don't mix up the friends!
Make sure you're comparing the right mileages.

STEP 2

1. Calculate Nachelle's mileage.
2. Calculate Zachary's mileage.
3. Compare the mileages.

STEP 3

Nachelle drives **196.3 miles** using **13 gallons** of gas.
To find her mileage, we **divide** the **total miles** by the **total gallons**.
This tells us how many miles she gets *per* gallon.
It's like figuring out how much of a single pie each person gets if you divide the pie evenly!

STEP 4

196.3 miles13 gallons=15.1 miles per gallon\frac{196.3 \text{ miles}}{13 \text{ gallons}} = 15.1 \text{ miles per gallon} So, Nachelle gets **15.1 miles per gallon**.

STEP 5

Zachary's mileage is sneakily hidden in the table!
We can pick *any* two rows from the table to calculate his mileage.
Let's pick the first two rows.
He can drive 8787 **miles** with 33 **gallons** of gas, and he can drive 145145 **miles** with 55 **gallons** of gas.
That means he drove an *extra* 14587=58145 - 87 = 58 **miles** using an *extra* 53=25 - 3 = 2 **gallons** of gas.

STEP 6

To find his mileage, we **divide** the **extra miles** by the **extra gallons**. 58 miles2 gallons=29 miles per gallon\frac{58 \text{ miles}}{2 \text{ gallons}} = 29 \text{ miles per gallon} Zachary gets **29 miles per gallon**.
Let's double-check this with another pair of rows, just to be super sure!
Let's use the last two rows this time.
He drives an *extra* 261203=58261 - 203 = 58 **miles** using an *extra* 97=29 - 7 = 2 **gallons** of gas.

STEP 7

58 miles2 gallons=29 miles per gallon\frac{58 \text{ miles}}{2 \text{ gallons}} = 29 \text{ miles per gallon} Yep, **29 miles per gallon**!
We're good to go!

STEP 8

Nachelle gets **15.1 miles per gallon**, and Zachary gets **29 miles per gallon**.
To find the difference, we **subtract** Nachelle's mileage from Zachary's mileage.

STEP 9

2915.1=13.929 - 15.1 = 13.9 Zachary gets **13.9** more miles per gallon than Nachelle.

STEP 10

Nachelle's car gets **15.1** miles per gallon, which is **less** than Zachary's car by **13.9** miles per gallon.

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