Amy has a total of 560 marbles, She has five times as many small marbles as medium marbles. The number of large marbles is two more than three times the number of medium marbles. How many of each size does she have?

Let m = number of medium marbles

s = 5m
L = 3m +2
m + 5m + (3m+2) = 560
Solve for m, then s and L.

Thanks

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Full quiz please?

To solve this problem, we can use algebraic equations to represent the given conditions.

Let's denote the number of small marbles as S, the number of medium marbles as M, and the number of large marbles as L.

From the first condition, we know that Amy has five times as many small marbles as medium marbles. So, we can write the equation: S = 5M.

From the second condition, we know that the number of large marbles is two more than three times the number of medium marbles. So, we can write the equation: L = 3M + 2.

We are also given that Amy has a total of 560 marbles, so the sum of the three types of marbles should equal 560. We can write the equation: S + M + L = 560.

Now, we can substitute the value of S from the first equation into the third equation. S + M + L = 560 becomes 5M + M + L = 560.

Next, substitute the value of L from the second equation into the modified equation. 5M + M + (3M + 2) = 560.

Now, simplify the equation: 9M + 2 = 560.

To isolate M, subtract 2 from both sides of the equation: 9M = 558.

Divide both sides of the equation by 9: M = 62.

Now that we have found the value of M, we can substitute it back into the first and second equations to find the values of S and L.

From the first equation, S = 5M, substitute M = 62: S = 5 * 62 = 310.

From the second equation, L = 3M + 2, substitute M = 62: L = 3 * 62 + 2 = 188.

So, Amy has 310 small marbles, 62 medium marbles, and 188 large marbles.