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Gisele has $5.90 in quarters and nickels. If Gisele has 16 more nickels than quarters, how many quarters does she have?

 Aug 4, 2020
 #1
avatar+28021 
+1

q = quarters                  value = 25q

n = nickles =  (q+ 16)    value  =   5 (q+16)      values summed = 590

 

25q      +    5(q+16)       = 590      solve for   q

 Aug 4, 2020
 #3
avatar+169 
+3

Ahh, I see how you're doing it. Yes, guest, you can also do it in cents or just multiply by a 100 if you want cleaner numbers to work with. Nice catch!

Inspirational  Aug 4, 2020
 #2
avatar+169 
+2

Set:

 

\(n=\text{number of nickles}\\ q=\text{number of quarters}\)

Now, we can make a system of equations. We have:

\(\begin{align*} q+16&=n\\ 5.90&=0.05n+0.25q \end{align*}\)

I trust you can solve this yourself. If not, here it is even more simplified. Substituting \(n\) in, we have:

\(5.90=0.05(q+16)+0.25q\\ 5.90=0.05q+0.8+0.25q\\ 5.90-0.8=0.3q\)

Now finish on your own! :)

 Aug 4, 2020
 #4
avatar+1154 
+1

we can use algebra to form the equation 25x+5(x+16)=590 we distribute to get 25x+(5)(x)+(5)(16)=590 then it becomes 25x+5x+80=590 and we combine like terms to get (25x+5x)+(80)=590 then 30x+80=590 we then subtract 80 from both sides to get 30x+80−80=590−80 then 30x=510 finally we divide both sides by 30 to get 30x/30=510/30 then we have x=17 so we get that she has \(17\text{ Quarters}\)

 

and 33 nickels :)

 

 

To check we do 5*33+17*25 which simplifies into 165+425=590 so that means that our answer 

 Aug 4, 2020

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