Question

3) Jose has only dimes and quarters in his piggy bank. He has a total of $62.20 in his bank. The amount of
dimes is six more than three times the amount of quarters. How many dimes and quarters are there?

Answer 1

There are 342 dimes and 112 quarters in his piggy bank

Step-by-step explanation:

Jose has only dimes and quarters in his piggy bank

• He has a total of $62.20 in his bank
• The amount of  dimes is six more than three times the amount of quarters

We need to find how many dimes and quarters are there

Assume that the number of dimes is x and the number of quarters is y

∵ Jose has x dimes in his piggy bank

∵ Jose has y quarters in his piggy bank

∵ 1 dime = 10 cents

∵ 1 quarter = 25 cents

∵ He has a total of $62.20 in his bank

∵ 1 dollar = 100 cents

∴ He has a total = 62.20 × 100 = 6220 cents

- Multiply x by 10 and y by 25, then add the products and equate

   the answer by 6220

∴ 10x + 25y = 6220 ⇒ (1)

∵ The amount of  dimes is six more than three times the

   amount of quarters

- That means equate x by the sum of 3 times y and 6

∴ x = 3y + 6 ⇒ (2)

Now we have a system of equations to solve it

Substitute x in equation (1) by equation (2)

∴ 10(3y + 6) + 25y = 6220

- Simplify the left hand side

∴ 10(3y) + 10(6) + 25y = 6220

∴ 30y + 60 + 25y = 6220

- Add like terms in the left hand side

∴ (30y + 25y) + 60 = 6220

∴ 55y + 60 = 6220

- Subtract 60 from both sides

∴ 55y = 6160

- Divide both sides by 55

∴ y = 112

- Substitute the value of y in equation (2) to find x

∵ x = 3(112) + 6

∴ x = 336 + 6

∴ x = 342

There are 342 dimes and 112 quarters in his piggy bank

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

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