Question

Adam, Beth, and Carly walked a total of 10 miles collectively. Beth walked twice as far as Adam, and she walked a half a mile further than Carly. If a = number of miles Adam walks, b = number of miles Beth walks, and c = number of miles Carly walks, which equation is NOT true for this situation?

A) b = 2a
B) b = c + 0.5
C) 3a + c = 10
D) a + 2c = 10.5

Answer 1

D) a + 2c = 10.5

Explanation:

The variable a represents the number of miles Adam walks. Beth, represented by b, walks twice as many miles as Adam; this gives us the equation

b = 2a.

Beth also walks half a mile more than Carly (represented by c). This gives us the equation

b = c + 0.5

The total amount of miles from Adam (a), Beth (b) and Carly (c) is 10; this gives us the equation

a + b + c = 10

Substituting 2a in place of b, we have

a + 2a + c = 10

Combining like terms, we have

3a + c = 10

This leaves the last choice as the equation not true for the situation.

Answer 2

a=Adam; b=Beth; c=Carly
Beth walked 2 times as far as Adam
Beth walked 0.5 miles farther than Carly
b=2a
b=c+0.5
3a=b+a
3a+c=10
a+2c≠10.5
Solution: D. a+2c=10.5