Angel's car gets 32 miles per gallon and Mo's car gets 22 miles per gallon. When traveling from Morgan Run to Clinton, they both used a whole number of gallons of gas. What is the closest that Morgan Run and Clinton could be? How many gallons did Angel's car use? How many gallons did Mo's car use?

HOW DO I FIGURE THIS PROBLEM OUT?

I'm not sure but wouldn't it be for Angels car 30 and mos 20. Because its saying whole number .

Find a number than when divided by 32 gives a whole number and when divided by 20 gives a whole number. 160 will work.

Explain Bot Explain Bot answered
8 months ago

To solve this problem, we need to find a number that is both divisible by 32 and 22. This number will represent the distance between Morgan Run and Clinton in miles. Let's call this number "x".

One way to approach this problem is to find the least common multiple (LCM) of 32 and 22. The LCM is the smallest number that is evenly divisible by both 32 and 22.

To find the LCM:
1. List the prime factors of each number:
- Prime factors of 32: 2 x 2 x 2 x 2 x 2 = 2^5
- Prime factors of 22: 2 x 11 = 2 x 11 (no further simplification possible)

2. Take the highest power of each prime factor that appears in any of the numbers:
- Taking the highest power of 2, we have 2^5.
- Taking the highest power of 11, we have 11.

3. Multiply these prime factors to find the LCM:
- LCM(32, 22) = 2^5 x 11 = 32 x 11 = 352.

Therefore, the closest that Morgan Run and Clinton could be is 352 miles.

Now, to determine the number of gallons used by Angel's and Mo's cars, we divide the distance (352 miles) by their respective fuel efficiencies.

For Angel's car:
- Angel's car gets 32 miles per gallon, so we divide the distance (352 miles) by 32:
- Gallons used by Angel's car = 352 / 32 = 11 gallons.

For Mo's car:
- Mo's car gets 22 miles per gallon, so we divide the distance (352 miles) by 22:
- Gallons used by Mo's car = 352 / 22 = 16 gallons.

Therefore, Angel's car used 11 gallons of gas, and Mo's car used 16 gallons of gas.

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