6th grade math

Question

Mabel has 5/8 as many stickers as Claire. Claire has 5/6 as many stickers as Sarah. If the 3 girls have 226 stickers altogether, how many more stickers does Sarah have than Mabel? 

Answer 1

let Sarah has x stickers, then Claire has 5/6x, Mabel has 5/8*5/6x= 25/48 x

 

so x+5/6x+25/48x=226

48x/48+ 40x/48+25x/48=226

113x=10848

x=96

 

So Sarah has 96 stickers

Claire has 5/6*96 = 80 stickers

and Mavel has 5/8*80 = 50 stickers

Answer 2

Let's call the number of stickers Sarah has X.

 

Then Claire has 5/6(x) stickers and

 

Mabel has 5/8(5/6(x)) stickers.

 

All three together have 226 stickers.  Add them up.

 

5/8(5/6(x)) + 5/6(x) + x = 226

 

Multiply to get 25/48(x) + 5/6(x) + x = 226

 

Convert all x terms to common denominator of 48.

 

25/48(x) + 40/48(x) + 48/48(x) = 226

 

Combine like terms

113/48(x) = 226

 

Multiply both sides by reciprocal of 113/48 and simplify.

 

x = 96

 

So, Sarah has 96.  Plug 96 back into original fractions for Claire and Mabel and you will see that Claire has 80 and Mabel has 50.

 

 

To find how many more stickers does Sarah have than Mabel?  96-50 = 46