he points on line a represent combinations of nickels and dimes that equal 8 total coins. The points on line b represent the combinations of nickels and dimes that have a total value of 50 cents.

Question

How many nickels and dimes would you need to have both a total of 8 coins and a value of 50 cents?
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Number of nickels
Number of dimes
nickels and
dimes would both total to 8 coins and have a total value of 50 cents.

Answer 1

To find the combinations of nickels (x) and dimes (y) that total 8 coins and 50 cents, we can set up two equations based on the information provided.

1. The total number of coins (nickels + dimes) is 8: \[ x + y = 8 \]

2. The total value in cents (nickels are worth 5 cents, dimes are worth 10 cents) is 50 cents: \[ 5x + 10y = 50 \]

Now, we can solve these two equations.

1. From the first equation, we can express \(y\) in terms of \(x\): \[ y = 8 - x \]

2. Substitute \(y\) into the second equation: \[ 5x + 10(8 - x) = 50 \] Simplifying this: \[ 5x + 80 - 10x = 50 \] \[ -5x + 80 = 50 \] \[ -5x = 50 - 80 \] \[ -5x = -30 \] \[ x = 6 \]

3. Now substitute \(x = 6\) back into the first equation: \[ 6 + y = 8 \] \[ y = 8 - 6 = 2 \]

Thus, you would need 6 nickels and 2 dimes to have both a total of 8 coins and a total value of 50 cents.