Question

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.
How many nickels and dimes would you need to have both a total of 8 coins and a value of 50 cents?
x
y
ab
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
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.