Word Problem

Question

grace had 3 times as many stickers in her collection as taylor. when grace gave 19 stickers to taylor, each girl had exactly the same amount. how many did the girls have altogether?

Answer 1

Let's label our variables g = Grace; a = taylor.

Here's what we know:

g = 3a

g - 19 = a + 19

Isolate g by adding 19 to both sides to the second equation:

g = a + 38

so:

g = 3a = a + 38

Isolate a (subtract a to both sides):

2a = 38

Divide both sides by 2:

a = 19

 

Now that we know Taylor's, we can find Grace's sticker count:

g = 3 * 19

g = 57

 

Check our answers:

59 - 19 = 19 + 19:

38 = 38

 

add them together:

57 + 19 = 76

Answer 2

Let s represent the number of stickers in Taylor's collection. Then Grace had 3s stickers. When Grace gave 19 stickers to Taylor, Taylor then had s + 19 stickers and Grace had 3s - 19 stickers left. Since they had the same amount then,

 

s + 19 = 3s - 19

 

Adding 19 to both sides, 

 

s + 38 = 3s.

 

Subtracting s from both sides,

 

38 = 2s.

 

Finally, dividing both sides by 2, we obtain

 

19 = s.

 

Hence, Taylor had 19 stickers and Grace had 3s = 3(19) = 57. Altogether, they had 19 + 57 = 76 stickers.