Emil and Nathaniel went into a store to buy spinners and bouncy balls. Emil bought 2 spinners and 3 bouncy balls for $4 and Nathaniel bought 1 spinner and 4 bouncy balls for $3. Write a system of equations to represent this situation. Solve the system of equations algebraically to determine the price of each spinner and the price of each bouncy ball.

Answer 1

Let's assume the price of one spinner is x and the price of one bouncy ball is y.

According to the given information, we can create two equations:

2x + 3y = 4 - Equation 1 (Emil's purchase)
x + 4y = 3 - Equation 2 (Nathaniel's purchase)

To solve this system of equations algebraically, we can use the substitution method.

From Equation 2, we can express x in terms of y:

x = 3 - 4y

Now, substitute x in Equation 1 with this expression:

2(3 - 4y) + 3y = 4

Simplify:

6 - 8y + 3y = 4

Combine like terms:

-5y + 6 = 4

Subtract 6 from both sides:

-5y = -2

Divide both sides by -5:

y = 2/5

Now, substitute this value of y back into Equation 2 to find x:

x + 4(2/5) = 3

Multiply 4 and (2/5):

x + 8/5 = 3

Subtract 8/5 from both sides:

x = 3 - 8/5

Convert 3 to 15/5:

x = 15/5 - 8/5

Simplify:

x = 7/5

Therefore, the price of one spinner is 7/5 (or $1.40) and the price of one bouncy ball is 2/5 (or $0.40).