Marianna has only nickels and quarters in her piggy bank. Their combined value is $9.15. Their combined weight is one pound. Ninety nickels weigh one pound. Eighty quarters weigh one pound. How many nickels does Marianna have in her piggy bank?

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rani01654 rani01654 · Answer 1 · 2019-12-05T11:18:20+01:00

Answer:

There are 63 nickels that Marianna have in her piggy bank.

Step-by-step explanation:

Let us assume that there are x nickels and y quarters in the bank.

Therefore, 0.05x + 0.25y = 9.15 ...... (1)

⇒ x + 5y = 183 ........ (2) {Multiplying both sides with 20}

Now, 90 nickels weighs 1 pound.

Then, x nickels weighs [tex]\frac{x}{90}[/tex] pounds

Again, 80 quarters weighs 1 pound .

Then, y quarters weighs [tex]\frac{y}{80}[/tex] pounds.

Given that, [tex]\frac{x}{90} + \frac{y}{80} = 1[/tex] ........ (3)

⇒ x + 1.125y = 90 ......... (4) {Multiplying both sides with 90}

Now, subtracting equation (4) from equation (2) we get,

3.875y = 93

⇒ y = 24.

Now, from equation (4) we get, x = 90 - 1.125 (24) = 63.

So, there are 63 nickels that Marianna has in her piggy bank. (Answer)