To solve this problem, you must set up a system of equations with the information that you have been given. It says that you have a total of $7.00, so:
7.00 = .25Q + .10D with Q meaning the number of quarters and D meaning the number of dimes
or, to make it easier, multiply the whole equation by 100 and it will remove the decimals:
700 = 25Q + 10D
The problem also says that there are 46 coins total, so:
46= Q + D
If you multiply the second equation by 10, and subtract it from the first equation, it eliminates the D and you can solve the equation for Q.
700= 25Q + 10D
-460= 10Q + 10D =
So now, if you plug the 16 into either of the first equations, you can solve for D.
46= (16) + D
So there are thirty dimes and sixteen quarters.
from the given:
700=(46-q)(10)+25q <----substituting d in the equation 700=10d+25q with 46-q
16 quarters & 30 dimes
let x = number of dimes
let y = number of quarters
x + y = 46 coins
y = 46 - x
x(.10) + y(.25) = $7.00
substitute for y
x(.10) + (46 - x)(.25) = 7.00
.10x + 11.5 -.25x = 7.00
add like terms:
11.50 - 7 = .25x - .10x
4.50 = .15x
4.50/.15 = x
30 = x
Answer: There are 30 dimes and (46 -x which is 46 - 30) 16 quarters
Let q = number quarters so 46 - q = number of dimes so the value of the quarters = 25q and the value of the dimes = 10(46 - q) so now add the value of the quarters and dimes together and this must equal 700 (I expressed everything in pennies) so now you have an equation to solve for q:
25q + 10(46 - q) = 700
25q + 460 - 10q = 700 (distribute the 10)
15q + 460 = 700 (combine similar terms)
15q = 240 (subtract 460 from both sides)
q = 16 (divide both sides by 15)
so you have 16 quarters and 30 dimes--now check your answer to see if you have $7.00!
16 quarters, 30 dimes.
well the answer is 16 quarters which equals 4 dollars. 4 quarters per dollar equals 16.. there are 30 dimes which equal 3 dollars because there are 10 dimes per dollar