A childs piggy back contains 19 coins considered of nickels dimes and quarters the total amount of money in the bank is $3.05 if the number of quarters is 1 more than twice the number of nickels

Question

find the number of each type of coin in the bank?

please solve it by using two variables x and y and by using substitution method

Answer 1

Let "x" be the number of nickels, let "y" be the number of dimes, and let "z" be the number of quarters.

Then the three equations we are are:

x + y + z = 19

x(0.05) + y(0.10) + z(0.25) = 3.05

z = 2x + 1

Starting with:

x + y + z = 19 we can plug in "2x + 1" in place of "z" to get:

x + y + (2x + 1) = 19 and we can simplify to get:

y = 18 - 3x

Then, using:

x(0.05) + y(0.10) + z(0.25) = 3.05 we can multiply both sides of the equation by 20 to get:

x + 2y + 5z = 61 then we can plug in "2x + 1" in place of "z" to get:

x + 2y + 5(2x + 1) = 61

11x + 2y = 56

Then, we can plug in "18 - 3x" for "y" to get:

11x + 2(18 - 3x) = 56

5x + 36 = 56

5x = 20

x = 4

Since y = 18 - 3x we can plug in x = 4 to find y, y = 18 - 12 = 6

Since z = 2x + 1 we can plug in x = 4 to find z, z = 8 + 1 = 9

So 4 nickels, 6 dimes, and 9 quarters