9 James has \( \$ 10 \) in 5-cent and 10-cent coins in his change jar and counts 157 coins in total. How many 10-cent coins does he have?

To solve this problem, let's denote the number of 5-cent coins as \( x \) and the number of 10-cent coins as \( y \). We have two equations based on the information provided: 1. \( x + y = 157 \) (the total number of coins) 2. \( 0.05x + 0.10y = 10 \) (the total amount of money) To simplify, we can multiply the second equation by 100 to avoid decimals: \( 5x + 10y = 1000 \) Now we can simplify it further: \( x + 2y = 200 \) (dividing everything by 5) Now, we have a system of equations: 1. \( x + y = 157 \) 2. \( x + 2y = 200 \) Next, we can subtract the first equation from the second: \[ (x + 2y) - (x + y) = 200 - 157 \] This simplifies to: \[ y = 43 \] Now, substituting \( y = 43 \) back into the first equation to find \( x \): \[ x + 43 = 157 \] This leads to: \[ x = 157 - 43 = 114 \] So, James has \( 43 \) 10-cent coins.