#### Question

# Algebra word problemm .?

Your piggy bank has a total of 46 coins in it; some are dimes and some are quarters. If you have a total of $7.00, how many quarters and how many dimes do you have?

#### Answer

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 =

240= 15Q

16= Q

So now, if you plug the 16 into either of the first equations, you can solve for D.

46= (16) + D

30= D

So there are thirty dimes and sixteen quarters.

from the given:

700=10d+25q

46=d+q

the solution:

d=46-q

700=(46-q)(10)+25q <----substituting d in the equation 700=10d+25q with 46-q

700=460-10q+25q

700=460+15q

700-460=15q

240=15q

16=q

46-16=d

30=d

Final answer:

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