26 coins; nickels and dimes how many coins of each

Question

Phillip has 26 dimes and quarters in his desk, totaling $3.65. He wrote a system of equations to represent this situation; letting x represent the number of dimes and y represent the number of quarters.

Answer 1

In order to solve this problem, you have to create a system of equations. Given that you have a total of 26 dimes and quarters which have a total value of $3.65, you can write conclude the following:

let y = the number of quarters and x = the number of dimes

x + y = 26 (since you have a total of 26 quarters and dimes)

.25y + .10x = 3.65 (the total value of the coins is $3.65 with each quarter and dime being $.25 and $.10 respectively)

After this, you can multiply the second equation by a factor of 10 or 4 and subtract it from the first equation to eliminate a variable. Then, solve for the remaining variable. I hope this helps!

Answer 2

This is a word problem which must be taken step-by-step....

1. There is a total of 26 coins:
2. x = the number of dimes
3. 26 - x = the number of quarters
4. The sum of all these coins totals $3.65:
5. Total value of dimes is:
6. Total number of coins, in this case "x"
7. Multiplied by the value of each of these coins, 10¢
8. 0.10x
9. Total value of quarters is:
10. Total number of coins, in this case ( 26 - x )
11. Multiplied by the value of each of these coins, 25¢
12. 0.25 ( 26 - x )
13. Total value of all the coins together is:
14. The value of all the dimes together, 0.10x
15. Added to the value of all the quarters together, 0.25 ( 26 - x )
16. 0.10x + 0.25 ( 26 - x ) = 3.65
17. 0.10x + 6.50 - 0.25x = 3.65
18. 6.50 - 0.15x = 3.65
19. -0.15x = -2.85
20. x = 19

Therefore, we find that there are 19 dimes totaling 19 x 10¢ = $1.90. To find the number of quarters, we apply the second piece which we found... ( 26 - x ) = 26 - 19 = 7 quarters. The total value of these quarters is 7 x 25¢ = $1.75