Marcia has 84 less than three times as much as Sue together they have 132 how much money does Marcia have?

Answer 1

Sue has Z.

Marcia has (3Z - 84), three times as much as Sue, minus 84.

Together their amounts equal 132.

So,

The amount Sue has plus the amount Marcia has is 132 or,

Z + (3Z - 84) = 132

Then,

Z + 3Z = 132 + 84 (minus 84 from one side of the expression, and add it to the other side)

Z + 3Z = 216

(Z + 3Z)/Z = 216/Z (divide both sides by Z to get one Z on one side)

Z/Z + 3Z/Z = 216/Z (or written like this)

1 + 3 = 216/Z

4 = 216/Z

4 x Z = (216/Z) x Z (multiply both sides by Z)

4Z = 216

4Z/4 = 216/4 (divide by 4 to isolate Z)

Z = 54

So, Sue has 54, therefore if Marcia has (3Z - 84), then 3 x 54 - 84, which is 78.

So, Marcia has 78

We can check that together, 54 plus 78 equals 132.