Question

A bag is filled with purple and yellow marbles. There are 61 marbles in the bag. If there are 9 more purple marbles than yellow marbles, find the number of purple marbles and the number of yellow marbles in the bag. Use x as your variable.

What is the equation?

Answer 1

Yellow marbles = 26

Purple marbles = 35

Explanation:

`let \: no \: of \: yellow \: marbles \: = x \\ and \: no \: of \: purple \: marbles \: = y \\ \\ total \: marbles \: = 61 \\ \\ \implies \: x + y = 61.....(1) \\ \\ no \: of \: purple \: marbles \: are \: 9 \: more \\ \: than \: yellow \: marbles \\ \\ \implies \: y = x + 9....(2) \\ \\ from \: equations \: (1) \: and \: (2) \\ \\ \\ x + (x + 9) = 61 \\ \\ \implies \: 2x + 9 = 61 \\ \\ \implies \: 2x = 61 - 9 \\ \\ \implies \: 2x = 52 \\ \\ \implies \: x = (52)/(2) \\ \\ \implies \: x = 26 \\ \\ \implies \: x + 9 = 26 + 9 = 35 \\ \\ \implies \: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \: \: \:\: \: \\ no \: of \: yellow \: marbles = 26 \\ \ no \: of \: purple \: marbles = 35`