Every evening jenna emptys her pockets and puts her change in a jar. At the end of the week she counts her money. One week she had 40 coins, all of them dimes and quarters. When she added them up, she had a total of $7.75. How many quarters did jenna have?

Question

anonymous · Answer

d=number of dimes
q=number of quarters

kirbykirby · Answer

1st equation: 
d + q = 40 , does this make sense?

anonymous · Answer

Yea

kirbykirby · Answer

2nd equation:
one dime = $0.10
one quarter = $0.25

so, the dollar $ amount in dimes you have is 0.10x
and the dollar amount in quarters you have is 0.25y
So, the total amount in quarter and dimes is 0.10x + 0.25y = 7.75

anonymous · Answer

Ok i see

anonymous · Answer

How do we find out how many quarters we had??

kirbykirby · Answer

(sorry I accidentally replaced d and q  with x and y... so you should have 0.10d + 0.25q = 7.75) The number of quarters is q, But you have 2 equations and 2 unknowns. So you can do like in the previous problem... and solve for d and q:

d + q = 40
0.10q + 0.25q = 7.75

anonymous · Answer

@kirbykirby

kirbykirby · Answer

solve for q in both equations:
equation 1:

$$d + q = 40\
d + q - d = 40 - d\
q = 40 - d$$

second equation:
$$0.10d + 0.25q = 7.75\
0.10d + 0.25q - 0.10d = 7.75 - 0.10d\
0.25q = 7.75 - 0.10d$$
$$\frac{0.25q}{0.25} = \frac{7.75 - 0.10d}{0.25}\ \, \
q = \frac{7.75-0.10d}{0.25}$$

Now equate both equations:
$$40 - d = \frac{7.75-0.10d}{0.25} \ \, \
0.25(40-d)=7.75-0.10d\ \, \
10-0.25d = 7.75 - 0.10d\
-0.25d+0.10d=7.75-10\
-0.15d=-2.25\
d=\frac{-2.25}{-0.15}\
d=15
$$
Now back to the first equation, since you know d:
$$q + d = 40\
q + 15 = 40\
q = 40 - 15\
q = 25$$