Question

I NNEEEDDDDDD HELPPPPP PLEASEEEE

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.

Answer 1

193 = 7s + 8l ( Grad Party Equation)

92 = 8s + 2l (Father's Day Equation)

The small balloon bouquet uses 7 balloons and the large one uses 18 balloons

Explanation:

First we need to separate something, I chose l...

• 92 = 8s + 2l
• 2l = 92 - 8s
• l = 46 - 4s

...and we can replace this for l in the other equation!

• 193 = 7s + 8( 46 - 4s )
• 193 = 7s + 368 - 32s
• -175 = -25s
• 7 = s

Now that we have found the number of balloons needed for a small bouquet we can place that in an equation to find out how many balloons it takes to make a large bouquet.

• l = 46 - 4(7)
• l = 46 - 28
• l = 18

Now just to make sure we got that right. Just check them!

Grad Party Equation

• 193 = 7s + 8l
• 193 = 7(7) + 8(18)
• 193 = 49 + 144
• 193 = 193

We got one right and the other one...

Fathers Day Equation

• 92 = 8s + 2l
• 92 = 8(7) + 2(18)
• 92 = 56 + 36
• 92 = 92

We got both right yay!

Answer 2

The small balloon bouquet uses 7 balloons and the large one uses

18 balloons.

Explanation:

Let's say that small balloon bouquets are S and large balloon bouquets are L. For the graduation party the employee assembled 6 small bouquets and 6 large bouquets, the total number of balloon used is 150. To put the sentence into an equation will be:

6S + 6L= 150

S+L= 25 ----> 1st equation

For Father's Day, the employee uses 6 small bouquet and 1 large bouquet, the total number of balloons used is 60. The equation will be:

6S + 1L= 60

1L= 60- 6S ----> 2nd equation

We can solve the number of small balloon bouquet by substitute the 2nd equation into 1st. The calculation will be:

S+L = 25

S+ (60-6S)= 25

-5S= 25-60

-5S= -35

S= -35/-5

S=7

Then we can find L by substitute S value to 1st or 2nd equation.

S+L=25

7+L=25

L=18

Hope this helps ;)