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.
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.

Answer 1

Answer:

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

Step-by-step explanation:

i) Let the number of small marbles be x

ii) let the number of medium marbles be y

iii) let the number of large marbles be z

iv) Amy has 5 times as many small marbles as medium marbles therefore we can write  5y = x

v) the number of large marbles is two more than than three times the number of medium marbles therefore we can write

   z = 3y + 2

vi) Amy has a total of 560 marbles therefore we can write x + y + z = 560

vii) Therefore from i) we can write x  = 5y

viii) using vii) and v) in vi) we can write

    x + y + z  = 5y + y + 3y + 2 = 560

ix) Therefore 9y = 558   .... therefore y = $\frac{558}{9}$ = 62

x) Therefore from i) we get x  = y $\times$ 5 = 62 $\times$ 5 = 310

xi) Therefore z  = (3 $\times$ 62) + 2 =  188

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