+4 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.
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.
+539 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.
