Question

Trey can drive his car 140 miles on 4 gallons of gas. True of False: At this rate, Trey could drive 195 miles on 6 gallons of gas. ________ At this rate, Trey would need 5 gallons of gas to drive 165 miles._______ At this rate, if gas costs 3.45 per gallon, it would cost $27.60 to drive 260 miles._______

Answer 1

For every 140 miles, Trey uses 4 gallons:
140:4
We can simplify this ratio to 1 gallon by dividing each side by 4
35 miles : 1 gallon
1) To find out the miles travelled in 6 gallons, we multiply ea b side by 6
35*6 = 210miles : 1*6 = 6gallons
So it is false.

2) For 5 gallons, we multiply each side by 5
35*5 = 175miles : 1*5 = 5gallons
Once again, it is false

3) We modify the ratio for price
35 miles : 1 gallon
35 miles : 3.45 dollars
And then we work in reverse - instead of multiplying the ratio to reach a certain number, we divide a certain number by the ratio
$27.6/3.45 = 8
For the question to be true, each side has to become
260 miles : 27.6 dollars when multiplied by 8
However, 35*8 = 280, not 260, so the statement is false.