Question

hw - systems substitution
toby’s piggy bank contains only 5 cent and 10 cent coins. if it contains 60 coins with a total value of $3.75, find the number of each type of coin.
let x and y be the number of 5 cent and 10 cent coins respectively.
well done!
first solve for y to find the number of 10 cent coins.
equation 1: x + y = 60
equation 2: 5x + 10y = 375 or alternatively 0.05x + 0.1y = 3.75
enter your next step here

Explanation:

Step1: Solve Equation 1 for y

From \( x + y = 60 \), we can express \( y \) in terms of \( x \) by subtracting \( x \) from both sides. So, \( y = 60 - x \).

Step2: Substitute y into Equation 2

Equation 2 is \( 5x + 10y = 375 \) (or \( 0.05x + 0.1y = 3.75 \)). Substitute \( y = 60 - x \) into this equation:

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Step3: Find y using x

Now that we know \( x = 45 \), substitute \( x \) back into \( y = 60 - x \):
\( y = 60 - 45 = 15 \)

Answer:

The number of 5 - cent coins (\( x \)) is 45 and the number of 10 - cent coins (\( y \)) is 15.