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Colossal Elementary School had a mother/daughter painting weekend. On Saturday, eight mothers worked with 12 daughters to paint 220 square feet of a large mural on a wall in the gymnasium. The next day, six moms worked with eight daughters to paint another 152 square feet of the mural in the gym.

Write and solve a system of equations to find how many square feet each mom painted and how many square feet each daughter painted. Assume all moms painted at the same rate and all daughters painted at the same rate.

Colossal Elementary School had a motherdaughter painting weekend On Saturday eight mothers worked with 12 daughters to paint 220 square feet of a large mural on class=

Respuesta :

Answer:

Mothers painted 8 square feet

Daughters painted 13 square feet

Step-by-step explanation:

Let m be the  square feet painted by mom

and d be the square feet painted by daughters

On Saturday, eight mothers worked with 12 daughters to paint 220 square feet

So, 8m  + 12d = 220

The next day, six moms worked with eight daughters to paint another 152 square feet

So, 6m + 8d = 152

We have two equation. solve for m  and d

8m  + 12d = 220 ---------> equation 1

6m + 8d = 152 --------> equation 2

Apply elimination method, multiply the first equation by 3  and second equation by -4

24m + 36d = 660

-24m -32d = -608

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           4d = 52

divide both sides by 4

so d= 13

Now we solve for m, plug in 13 for d

8m  + 12d = 220

8m  + 12(13) = 220

8m  + 156 = 220

Subtract 156 on both sides

8m = 64

Divide both sides by 8

m = 8

Mothers painted 8 square feet

Daughters painted 13 square feet

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