word problems

Question

Grace is 4 inches taller than her sister.The sum of their heights is 118

inches.How tall is Grace?

Answer 1

Let's use G for Grace's height and S for her sister's height. You have two variables, so you need two equations.

 

G = S + 4, because Grace is 4 inches taller than her sister

G + S = 118, because their heights add up to 118 inches

 

Now you can use substitution to solve. You know from the first equation that G=S+4, so you can substitute S+4 in for G in the second equation and end up with only one variable. 

 

(S+4) + S = 118

 

Combining your like terms gives you

 

2S = 114

S = 57

 

The problem asks for Grace's height, which we denoted as G, so now you have to plug 57 in for S in one of the original equations to find G.

 

G = 57 + 4

G = 61

 

So Grace is 61 inches tall, which is easier to understand if you write it as 5 feet, 1 inch, or 5'1".