Lincoln has $0.90 worth of nickels and dimes. He has a total of 14 nickels and dimes altogether. By following the steps below, determine the number of nickels, x, commax, and the number of dimes, y, commay, that Lincoln has.

Question

Lincoln has $0.90 worth of nickels and dimes. He has a total of 14 nickels and dimes altogether. By following the steps below, determine the number of nickels, x, commax, and the number of dimes, y, commay, that Lincoln has.

Answer 1

Let's say the value of each nickel is $0.05 and the value of each dime is $0.10.

Step 1: Write two equations based on the given information.
The total value of nickels is 0.05x and the total value of dimes is 0.10y.
0.05x + 0.10y = 0.90 (equation 1)
The total number of nickels and dimes is 14.
x + y = 14 (equation 2)

Step 2: Solve the system of equations.
Multiply equation 2 by 0.05 to make the coefficients of x the same in both equations:
0.05x + 0.05y = 0.70 (equation 3)

Subtract equation 3 from equation 1 to eliminate x:
0.10y - 0.05y = 0.90 - 0.70
0.05y = 0.20
y = 0.20 / 0.05
y = 4

Substitute the value of y into equation 2:
x + 4 = 14
x = 14 - 4
x = 10

So Lincoln has 10 nickels and 4 dimes.

Answer 2

find another conbination

Answer 3

Let's try another combination.

Using the same equations as before:

0.05x + 0.10y = 0.90 (equation 1)
x + y = 14 (equation 2)

We can substitute x = 14 - y into equation 1:

0.05(14 - y) + 0.10y = 0.90
0.70 - 0.05y + 0.10y = 0.90
0.05y + 0.70 = 0.90
0.05y = 0.20
y = 0.20 / 0.05
y = 4

Substituting y = 4 into equation 2:

x + 4 = 14
x = 14 - 4
x = 10

So another combination is 10 nickels and 4 dimes.

Answer 4

find another combination that equals coins

Answer 5

Let's try to find another combination that equals 14 coins.

Using the same equations:

0.05x + 0.10y = 0.90 (equation 1)
x + y = 14 (equation 2)

We can try substituting different values of x and y into equation 2 to find another combination that satisfies both equations.

Let's try y = 12 and x = 2:

2 + 12 = 14 (equation 2)

This combination satisfies equation 2. Now let's substitute these values into equation 1:

0.05(2) + 0.10(12) = 0.90
0.10 + 1.20 = 0.90

This combination does not satisfy equation 1, so let's try another combination.

Let's try y = 10 and x = 4:

4 + 10 = 14 (equation 2)

This combination satisfies equation 2. Now let's substitute these values into equation 1:

0.05(4) + 0.10(10) = 0.90
0.20 + 1.00 = 0.90

This combination also does not satisfy equation 1.

It seems that there are no other combinations of nickels and dimes that satisfy both equations. Thus, the original combination of 10 nickels and 4 dimes is the only valid solution.