a. The expression y=5x represent the number of small marbles she has.
b. The expression z=3x+2 represents the number of large marbles she has.
c. Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
a. Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
Medium marbles = x
Let,
Small marbles = y
According to given statement;
She has five times as many small marbles as medium marbles.
y = 5x Eqn 1
The expression y=5x represent the number of small marbles she has.
b. Write an algebraic expression to represent the number of large marbles she has.
Let,
Large marbles = z
The number of large marbles is two more than three times the number of medium marbles.
z = 3x+2 Eqn 2
The expression z=3x+2 represents the number of large marbles she has.
c. If Amy has a total of 560 marbles, how many of each size does she have?
x+y+z= 560 Eqn 3
Putting value of y and z from Eqn 1 and 2 in Eqn 3
[tex]x+(5x)+(3x+2)=560\\x+5x+3x+2=560\\9x=560-2\\9x=558[/tex]
Dividing both sides by 9
[tex]\frac{9x}{9}=\frac{558}{9}\\x=62[/tex]
Putting x=62 in Eqn 1
[tex]y=5(62)\\y=310[/tex]
Putting x=62 in Eqn 2
[tex]z=3(62)+2\\z=186+2\\z=188[/tex]
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Keywords: linear equation, substitution method
Learn more about substitution method at:
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