Question 214299
Jessica found $52.25 in the parking lot. 
There was 3 times as many $1 bills as $5 bills,
 one-half as many quarters as $1 bills,
 and two more dimes than $1 bills.
 How many $5 bills did Jessica find?
:
Let c = no. of $1 bills
Let f = no. of $5 bills
Let d = no. of dimes
Let q = no. of quarters
;
Write an equation for each statement:
:
Jessica found $52.25 in the parking lot.
1c + 5f + .10d + .25q = 52.25
; 
There was 3 times as many $1 bills as $5 bills,
c = 3f
or
f = {{{1/3}}}c
:
 one-half as many quarters as $1 bills,
q = .5c
:
 two more dimes than $1 bills. 
d = c + 2
:
Using the equation: 1c + 5f + .10d + .25q = 52.25
Substitute for f, d, and q, find c
1c + 5({{{1/3}}}c) + .10(c+2) + .25(.5c) = 52.25
:
1c + {{{5/3}}}c + .1c + .2 + .125c = 52.25
;
1.225c + {{{5/3}}}c = 52.25 - .2
:
1.225c + {{{5/3}}}c = 52.05
: 
Get rid of the denominator, multiply equation by 3, results:
3(1.225)c + 5c = 3(52.05)
:
3.675c + 5c = 156.15
:
8.675c = 156.15
c = {{{156.15/8.675}}}
c = 18 ea $1 bills
:
How many $5 bills did Jessica find?
f = {{{1/3}}}c
f = {{{1/3}}}* 18
f = 6 ea $5 bills
:
:
Ill let you check the solution in the original equation with substitution