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

An employee at a party store is assembling balloon bouquets. For a graduation party, he assembled 7 small balloon bouquets and 8 large balloon bouquets, which used a total of 193 balloons. Then, for a Father's Day celebration, he used 92 balloons to assemble 8 small balloon bouquets and 2 large balloon bouquets. How many balloons are in each bouquet?

The small balloon bouquet uses___  balloons and the large one uses___  balloons.

 Jan 26, 2021
 #1
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

One Friday night, two large groups of people called Livingston Taxi Service. The first group requested 1 sedan and 2 minivans, which can seat a total of 16 people. The second group asked for 3 sedans and 2 minivans, which can seat a total of 24 people. How many passengers can each type of taxi seat?

A sedan can seat ___  people, and a minivan can seat ___  people.

 Jan 26, 2021
 #2
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Say the number of balloons in a small bouquet is x and the number in a large bouquet is y.

The equations we have are

7x+8y=193 and

8x+2y=92.

On the second equation, isolating y we get 2y=92-8x or y=46-4x.

Plug that in our first equation to get

7x+8(46-4x)=193.

7x+368-32x=193

-25x+368=193

-25x=-175

x=7

Now that we have x, we can solve for y.

8(7)+2(y)=92

56+2(y)=92

2(y)=36

y=18.

 Jan 26, 2021

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