Question

A piggy bank at the flea market has 5 more than double the number of Dimes than quarters. The money in the piggy bank is worth $7.70. how many dimes and quarters are in the piggy bank?

Answer 1

To find the number of dimes and quarters in the piggy bank, we can solve an algebraic equation. Let 'q' represent the number of quarters, and '2q + 5' represent the number of dimes. By converting the money value into cents and setting up an equation, we can find the values of 'q' and '2q + 5'. The solution is 16 quarters and 37 dimes.

Step-by-step explanation:

We can solve this problem using algebraic equations. Let's start by assigning variables to represent the number of dimes and quarters in the piggy bank. Let's say the number of quarters is 'q', and the number of dimes is '2q + 5' since there are 5 more than double the number of dimes than quarters.

Next, let's convert the money value into cents. Each quarter is worth 25 cents and each dime is worth 10 cents. The total value in cents is 770.

Now we can write an equation based on the total value: 25q + 10(2q + 5) = 770. Simplifying the equation, we get 25q + 20q + 50 = 770. Combining like terms, we have 45q + 50 = 770. Subtracting 50 from both sides, we get 45q = 720. Dividing both sides by 45, we find that q = 16.

So, there are 16 quarters in the piggy bank. To find the number of dimes, we can substitute q into the expression 2q + 5. 2(16) + 5 = 32 + 5 = 37. Therefore, there are 37 dimes in the piggy bank.

Answer 2

Let d represents the dimes and q represents the quarters.

As per the statement:

A piggy bank at the flea market has 5 more than double the number of Dimes than quarters.

⇒q = 2d +5 ......[1]

It is also given that: The money in the piggy bank is worth $7.70.

⇒
`q+d = 7.70` ......[2]

Substitute equation [1] into [2] we have;

`2d+5+d = 7.70`

Combine like terms;

`3d +5 = 7.70`

Subtract 5 from both sides we get;

`3d = 2.70`

Divide both sides by 3 we get;

`d =\$0.90`

Substitute the values of d in equation in [1] we get;

q = 2(0.90) +5 = 1.80 + 5 = $6.80

Therefore, the dimes and quarters are in the piggy bank is $0.90 and $6.80