A jar cointains dimes and quarters .the total number of coins in the jar is 25 .the total value of the coins is $3.70 how many of each type of coin are in the jar

d + q = 25

10 d + 25 q = 370

solve the system for d and q
... multiplying 1st equation ... 10 d + 10 q = 250

subtract equations to eliminate d ... 15 q = 120

To solve this problem, we can set up a system of equations. Let's represent the number of dimes as "D" and the number of quarters as "Q."

Based on the information given in the problem:

Equation 1: D + Q = 25 (since the total number of coins in the jar is 25)
Equation 2: 0.10D + 0.25Q = 3.70 (since the total value of the coins is $3.70)

Now, we can solve this system of equations using substitution or elimination.

Using substitution method:

From Equation 1: D = 25 - Q

Substituting this into Equation 2:

0.10(25 - Q) + 0.25Q = 3.70
2.50 - 0.10Q + 0.25Q = 3.70
0.15Q = 3.70 - 2.50
0.15Q = 1.20
Q = 1.20 / 0.15
Q = 8

Now that we know Q = 8, we can substitute this value back into Equation 1:

D + 8 = 25
D = 25 - 8
D = 17

So, there are 17 dimes and 8 quarters in the jar.

To find the number of dimes and quarters in the jar, we can set up a system of equations based on the given information.

Let's assume:
- The number of dimes in the jar is represented by the variable 'd.'
- The number of quarters in the jar is represented by the variable 'q.'

From the problem statement, we have two pieces of information that we can use to create two equations:

1. The total number of coins in the jar is 25:
d + q = 25

2. The total value of the coins is $3.70:
0.10d + 0.25q = 3.70

Now, we can solve this system of equations. We'll use the substitution method:

From equation 1, we can express 'd' in terms of 'q' by subtracting 'q' from both sides:
d = 25 - q

Substitute this expression for 'd' into equation 2:
0.10(25 - q) + 0.25q = 3.70

Simplify the equation:
2.50 - 0.10q + 0.25q = 3.70
0.15q = 1.20

Divide both sides by 0.15 to solve for 'q':
q = 1.20 / 0.15
q = 8

Now we know that there are 8 quarters in the jar. To find the number of dimes, substitute the value of 'q' into equation 1:

d + 8 = 25
d = 25 - 8
d = 17

Therefore, there are 17 dimes and 8 quarters in the jar.