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.
<u>Step-by-step explanation:</u>
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.
