Question

A man has 14 coins in his pocket, all of which are dimes and quarters. if the total value of his change is $1.70, how many dimes and how many quarters does he have?

Answer 1

To determine how many dimes and quarters the man has, set up a system of equations and solve simultaneously to find that the man has 12 dimes and 2 quarters.

Step-by-step explanation:

To solve the problem involving the man with 14 coins consisting of dimes and quarters, we will use a system of equations. Let's define d as the number of dimes and q as the number of quarters. Two equations can be described:

• The total number of coins is 14: d + q = 14.
• The total value of the coins is $1.70: 10d + 25q = 170 (since there are 100 pennies in one dollar, the value of the dimes and quarters must be converted into cents to match the total amount which is also in cents).

Solving these equations simultaneously, we subtract the first equation from the second equation multiplied by 10:

10d + 25q = 170 (second equation multiplied by 10)

10d + 10q = 140 (first equation multiplied by 10)

Subtracting the second equation from the first:
15q = 30

Dividing both sides of the equation by 15:

q = 2

Plugging the value of q into the first equation:

d = 14 - 2 = 12

Therefore, the man has 12 dimes and 2 quarters.

Answer 2

d + q = 14....d = 14 - q
0.10d + 0.25q = 1.70

0.10(14 - q) + 0.25q = 1.70
1.40 - 0.10q + 0.25q = 1.70
-0.10q + 0.25q = 1.70 - 1.40
0.15q = 0.30
q = 0.30 / 0.15
q = 2 <=== 2 quarters

d + q = 14
d + 2 = 14
d = 14 - 2
d = 12 <=== 12 dimes