Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. An employee at a party store is assembling balloo

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

An employee at a party store is assembling balloon bouquets. For a graduation party, he assembled 6 small balloon bouquets and 7 large balloon bouquets, which used a total of 203 balloons. Then, for a Father's Day celebration, he used 145 balloons to assemble 1 small balloon bouquet and 6 large balloon bouquets. How many balloons are in each bouquet?

Answer 1

6S + 7L = 203

1S + 6L = 145

 

Use elimination by multiplying the bottom equation by -6.

 

 6S + 7L = 203

-6S - 36L = -870

 

Add the two equations together. The S-terms will cancel out leaving only L-terms.

 

-29L = -667

 

Divide both sides by -29.

 

L = 23 large balloons!

 

Now plug in the L into one of the original equations.

 

S + 6(23) = 145

S + 138 = 145  (Now subtract 138 from both sides to isolate the  S)

S = 7 small balloons! 

 

I hope this helps!!