A crayon ratio of 7:2 Steve:Laura

Question

A crayon ratio of 7:2 Steve:Laura. Steve gives Laura 15 of his crayons now they both have an equal amount of crayons. How many crayons do they each have?

Answer 1

I think I understand. Steve and Laura initially had crayons in a ratio of 7:2. After Steve gives Laura 15 of his crayons, the both have equal amounts. Then, we want to know their final amounts? Or their initial amounts? I guess I will just answer both.

 

Let's write what we know in algebraic language. I will use "/" to mean division. I will use S for Steve's initial amount and L for Laura's initial amount.

 

S / L  =  7 / 2

S - 15  =  L + 15

 

I would use substitution. So, first solve the second equation for S in terms of L.

 

S  =  L + 30

 

Now, substitute into the first equation.

 

(L + 30) / L = 7 / 2

 

Multiply both sides by 2*L.

 

2*(L + 30)  =  7 * L

 

Distribute.

 

2L + 60 = 7L

 

Subtract 2L from both sides.

60 = 5L

Divide both sides by 5.

 

12 = L

 

Laura started with 12 crayons. Steve started with 30 more (Remember S = L + 30), so Steve began with 42 crayon. Indeed, we should check that 42/12 = 7/2.

 

After the transfer of crayons, they each would have 27 crayons.