Question

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.
A.Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
B. Write an algebraic expression to represent the number of large marbles she has.
C.If Amy has a total of 560 marbles, how many of each size does she have? Show your work.

Answer 1

a) The algebraic expression to represent the number of small marbles she has is w = 5x

b) The algebraic expression to represent the number of large marbles she has is y = 2 + 3x

c) The number of small marbles is 310 and number of medium marbles is 62 and number of large marbles is 188

Solution:

Let w represent the number of small marbles Amy has

Let x represent the number of medium marbles Amy has

Let y represent the number of large marbles Amy has

a) She has five times as many small marbles as medium marbles

Therefore,

Number of small marbles = five times as number of medium marbles

w = 5x --------- eqn 1

b) The number of large marbles is two more than three times the number of medium marbles

Number of large marbles = 2 + 3 times the number of medium marbles

y = 2 + 3x ------ eqn 2

c) Amy has a total of 560 marbles

Therefore,

w + x + y = 560 ------ eqn 3

Substitute eqn 1 and eqn 2 in eqn 3

5x + x + 2 + 3x = 560

9x + 2 = 560

9x = 560 - 2

9x = 558

Divide both sides of equation by 9

x = 62

Substitute x = 62 in eqn 1

w = 5(62)

w = 310

Substitute x = 62 in eqn 2

y = 2 + 3(62)

y = 2 + 186

y = 188

Thus, number of small marbles is 310 and number of medium marbles is 62 and number of large marbles is 188