Laura has 23 coins in a jar. The jar contains only dimes and quarters. If the coins are worth $4.85, how many dimes does Laura have?

Question

anonymous · Answer

let x be the number of dimes, and y be the number of quarters.

Since there are 23 coins, we know that:
$$x+y = 23$$Then, because the value of those coins is 4.85, we know that;
$$10x+25y = 485$$

Now we just have to solve this system of equations.

anonymous · Answer

Let x be the number of dimes and y be the number of quarters
So, x+y = 23
0.1x+0.25y = 4.85
10x+25y = 485
Solce simultaneously, to get 
x=6 and y = 17

anonymous · Answer

You could multiply the first equation by 10 to get:
$$10x+10y =230 $$Then subtract the two equations to get:
$$15y = 255 \iff y = 17$$
Now we know there are 17 quarters.  So there must be 6 dimes (since there were 23 coins in the jar)

amistre64 · Answer

23 coins

dimes and quarters

worth $4.85

d = (4.85 - 23(.25))/(.10-.25) = 6