Otis has a box of coins that he uses when he plays poker with his friends. the box containts 44 coins, consisting of pennies, dines, and quarters. the number of pennies is equal to the number of dimes. the total value is $4.37. how many of each denomination of coin does he have in the box

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carlosego carlosego · Answer 1 · 2018-07-13T12:58:51+02:00

For this case, the first thing we must do is define variables.

We have then:

x: number of pennies

y: number of dimes

z: number of quarters

We now write the system of equations:

the box containts 44 coins:

[tex] x + y + z = 44
[/tex]

The number of pennies is equal to the number of dimes:

[tex] x = y
[/tex]

the total value is $ 4.37:

[tex] 0.01x + 0.1y + 0.25z = 4.37
[/tex]

Solving the system of equations graphically, we obtain:

Let's rewrite equations 1 and 2:

[tex] x + x + z = 44

0.01x + 0.1x + 0.25z = 4.37
[/tex]

The intersection of the straight lines is the graphic solution

Note: see attached image

x = 17

z = 10

Then, the value of y is:

y = x = 17

Answer:

pennies = 17

dimes = 17

Quarters = 10