Arthur weighs 21 lbs more than lily. Their combined weight is 114 lb less than four times lilys weight. How much does lily weigh?

Question

Arthur weighs 21 lbs more than lily. Their combined weight is 114 lb less than four times lilys weight. How much does lily weigh?

Answer 1

I like to tell people to look for pieces that you can write expressions for, then re-read the problem to see how to put them together.

 

Arthur weighs 21 lbs more than lily.

A = L + 21

 

four times lily's weight

4L

 

114 lb less than four times lily's weight

4L - 114

 

Their combined weight

A + L

 

So:

A + L = 4L - 114

 

Simplify this second equation.

A - 3L = -114

 

The first equation gives you an expression for A than you can now substitute in the second one.

(A) = L + 21

so 

(L + 21) - 3L = -114

L - 3L = -114 - 21

-2L = -135

 

L = 67.5

 

Check:

Solve equation 1 for A

A = L + 21

A = 67.5 + 21 = 88.5

 

Check values in equation 2

A + L = 4L - 114

88.5 + 67.5 = 4 * 67.5 - 114

156 = 156      It works!