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

Dividing both sides by 9

Putting x=62 in Eqn 1

Putting x=62 in Eqn 2

Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Keywords: linear equation, substitution method
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Answer:
6 laps.
Step-by-step explanation:
On Monday she runs 2x + 8 miles, where x miles = the length of the trail.
On Tuesday she runs 4x + 4 miles and this is the same distance as Monday, so
2x + 8 = 4x + 4
4 = 2x
x = 2 miles which is the length of the trail.
So each day she runs 4(2) + 4 = 12 miles.
So on Saturday she runs 12/ 2 = 6 laps.
Answer:
Yes.
Step-by-step explanation:
The number 3 is a <u>natural number</u>, and all of these types of numbers are rational.
Another way to look at it is if a number can be <u>written as a fraction</u>, the number is rational.