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Crank
3 years ago
15

I have 8 pennies and some quarters, nickels, and dimes. The number of pennies plus nickels equals the number of dimes. I have 3

quarters for every 2 pennies and 3 dimes for every 2 quarters. How many coins are nickels?
Mathematics
2 answers:
Sati [7]3 years ago
7 0

Answer:8 pennies, 12 quarters, 18 dimes, so there are 10 nickels

Step-by-step explanation:

Darina [25.2K]3 years ago
5 0

There are five nickels.

Let <em>w</em> = the number of pennies; <em>x</em> = the number of nickels; <em>y</em> = the number of dimes; <em>z </em>= the number of quarters.

Then, we have three equations with four unknowns:

(1) <em>w</em> + <em>x = y </em>

(2) 3<em>w</em> = 2<em>z</em>

(3) 2<em>y</em> = 3<em>z</em>

However, there is a fourth <em>unstated </em>condition: <em>w</em>, <em>x</em>, y, and <em>z</em> must all be integers.

Assume that z = 6 (to avoid fractions).

From Equation (2), w = 4.

From Equation (3), y = 9.

Insert the values for <em>w</em> and <em>y</em> into equation (1).

4 + <em>x</em> = 9

x = 9 – 4 = 5

Thus, there are 4 pennies, 5 nickels, 9 dimes, and 6 quarters.

<em>Check</em>: 4 pennies + 5 nickels = 9 dimes

6 quarters + 4 pennies = 3 quarters for every 2 pennies

9 dimes + 6 quarters = 3 dimes for every 2 quarters

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