Answer:
Yellow marbles = 26
Purple marbles = 35
Step-by-step explanation:
[tex]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 = \frac{52}{2} \\ \\ \implies \: x = 26 \\ \\ \implies \: x + 9 = 26 + 9 = 35 \\ \\ \implies \: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \:\: \:\: \: \: \: \: \: \: \:\: \: \\ no \: of \: yellow \: marbles = 26 \\ \ no \: of \: purple \: marbles = 35[/tex]
