Amy has a collection of marbles in three sizes, small, medium, and large. 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.

Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.

Write an algebraic expression to represent the number of large marbles she has.

If Amy has a total of 560 marbles, how many of each size does she have? Show your work.

The explanation is very good yet misses the frequency.

The algebraic equation for small and large marbles are y=5x and z=3x+2. The number of small marbles is 310. The number of small marbles is 310. The number of large marbles is 188.

Step-by-step explanation:

From the given information, Amy has three sizes of marbles.

Let x represents the medium marbles, y as small marbles and z as large marbles.

The number of small marbles she has is 5 times more than medium marbles. Then the algebraic equation for small marbles:

⇒ y = 5x.

The number of large marbles she has is two more than three times. Then the algebraic equation for large marbles:

⇒ z=3x+2.

And the sum of three marbles is 560.

∴x+y+z=560.

To find each number of marbles, substitute the algebraic equation of y and z in the above equation.

⇒x+5x+3x+2=560.

9x+2=560.

9x = 560-2.

9x=558.

x = 62.

∴The number of medium marbles is 62.

The number of small marbles y = 5x.

⇒y = 5 (62)

y = 310.

∴The number of small marbles is 310.

The number of large marbles z = 3x+2.

⇒z = 3 (62) + 2

z = 186+2.

z=188.

∴The number of large marbles is 188.