Question

Ngo has a collection of dimes and quarters with a total value of $3.50. The number of dimes is seven more than the number of quarters. How many of each coin does he have?

Answer 1

The number of coins of quarters are 8 and The number of coins of dimes are 15

Explanation:

Let the number of coins of quarters be x

We are given that The number of dimes is seven more than the number of quarters

No. of dimes = x+7

1 quarter = $0.25.

x quarters = $0.25 x

1 dime = $0.10

(x+7) dimes = 0.10(x+7)

Now we are given that Ngo has a collection of dimes and quarters with a total value of $3.50.

`0.25 x+0.10(x+7)=3.50`

`0.25 x+0.10x+0.70=3.50`

`x=8`

x+7=8+7=15

Hence the number of coins of quarters are 8 and The number of coins of dimes are 15

Answer 2

Let us assume number of quarters coins = x.

We are given that number of dimes is seven more than the number of quarters.

Therefore, number of dimes coins = x+7.

Total value of all coins = $3.50.

We can setup an equation,

0.25 * number of quarter coins + 0.10 * number of dimes coins = 3.50.

0.25x + 0.10(x+7) =3.50

Distributing 0.10(x+7), we get

0.25x +0.10x +0.70 =3.50

Combining like terms, we get

0.35x + 0.70 = 3.50

Subtracting 0.70 from both sides, we get

0.35x + 0.70-0.70 = 3.50-0.70

0.35x = 2.80

Dividing both sides by 0.35

0.35x/0.35 = 2.80/0.35

x = 8.

Therefore, number of quarters = 8.

Number of dimes are 7 more than quarters = 8+7 = 15.

Therefore, 8 quarter and 15 dimes.