i have a total of 49 dimes and quarters. the value of quarters is the same value of my dimes. find the number of each coin

Question

anonymous · Answer

what are my equations?

whpalmer4 · Answer

okay, there are 49 coins, let's call the variables representing quarters and dimes $q$ and $d$ respectively.

$$q+d = 49$$

Agreed?

anonymous · Answer

I got that part (:

anonymous · Answer

Just the second equation that is stumping me

whpalmer4 · Answer

no problem.  what's the value of $q$ quarters (expressed in cents)?

whpalmer4 · Answer

1 quarter = 25 cents
2 quarters = 50 cents
$q$ quarters = ?

anonymous · Answer

25q...?

whpalmer4 · Answer

yes.  what is the corresponding expression for the value of the dimes?

anonymous · Answer

10d

whpalmer4 · Answer

right.  now, the problem says the value of the quarters is the same as the value of the dimes, right?  How could you express that?

anonymous · Answer

25q=10d

whpalmer4 · Answer

okay, so now you have two equations in two unknowns, and as one of them has coefficients of 1 for both variables, solving by substitution should be easy enough...

anonymous · Answer

Ohhhhh ok. THANKS SO MUCH! (:

whpalmer4 · Answer

got an answer for me?

anonymous · Answer

oh ok hold on

anonymous · Answer

Wait....wouldn't i have to divide the second equation by 25 or 10 for the variable to be on it's own?

anonymous · Answer

14 quarters, 35 dimes

whpalmer4 · Answer

14*25 + 35*10 = 350 + 350 = 700 so that is correct
equal value of quarters and dimes, and 14+35 = 49 coins in all.