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# i need help

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164
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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
+32709
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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
+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
+169
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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
+1164
+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