Write a system of equations to find how many square feet each mom painted and how many square feet each daughter painted.

Let the Number of Square feet Painted by each Mother be : M

Let the Number of Square feet Painted by each Daughter be : D

On Saturday : 8 Mothers worked with 12 Daughters and painted 220 Square feet

⇒ 8M + 12D = 220

Dividing the above Equation with 4

⇒ 2M + 3D = 55 [1]

On Sunday : 6 Mothers worked with 8 Daughters and painted 152 Square feet

⇒ 6M + 8D = 152

Dividing the above equation with 2

⇒ 3M + 4D = 76 [2]

Multiplying Equation [1] with 3, We get :

⇒ 6M + 9D = 165 [3]

Multiplying Equation [2] with 2, We get :

⇒ 6M + 8D = 152 [4]

Subtracting Equation [4] from Equation [3], We get :

⇒ (6M + 9D) - (6M + 8D) = 165 - 152

⇒ 6M + 9D - 6M - 8D = 13

⇒ D = 13

Substituting D = 13 in Equation [1] , We get :

⇒ 2M + 3(13) = 55

⇒ 2M + 39 = 55

⇒ 2M = 55 - 39

⇒ 2M = 16

⇒ M = 8

⇒ Number of Square feet Painted by each Mother : 8

⇒ Number of Square feet Painted by each Daughter : 13

step-by-step explanation:

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