SOLUTION: I am having trouble figuring out what these 2 word problems are trying to tell me to do normally I am ok with them but I am having trouble. I would really appreciate the help as so
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Question 781991: I am having trouble figuring out what these 2 word problems are trying to tell me to do normally I am ok with them but I am having trouble. I would really appreciate the help as soon as possible. If I am not supposed to put 2 questions in here just help me with one and it might help me understand the other. This is my first time using the site and I am desperate just to understand. Thank you in advance.
1. Jenny recieved $6.10 in tips one afternoon. All her tips were in quarters, dimes, and nickels. There were five less dimes than quarters and seven less nickels than dimes. How many of each kind of coin was there?
2. Grammy's change rack contained $8.80 in quarters, dimes, and nickels. There were two more than five times as many nickels as quarters and four less than twice as many dimes as quarters. How many of each kind of coin was in there in the change rack?
Thank you. :)
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. Jenny recieved $6.10 in tips one afternoon.
All her tips were in quarters, dimes, and nickels.
There were five less dimes than quarters and seven less nickels than dimes.
How many of each kind of coin was there?
:
Let q = no. of quarters, d = no. of dimes; and n = no. of nickels
:
Write an equation for each statement we will try solve in in terms of d:
;
"Jenny received $6.10 in tips one afternoon."
.05n + .10d + .25q = 6.10
;
" There were five less dimes than quarters"
d = q-5
we can also write this
q = d+5
:
"and seven less nickels than dimes."
n = d-7
:
Replace d and n in the 1st equation
.05(d-7) + .10d + .25(d+5) = 6.10
distribute and combine like terms
.05d - .35 + .10d + .25d + 1.25 = 6.10
.40d + .90 = 6.10
.40d = 6.10 -.90
.40d = 5.20
d = 5.2/.4
d = 13 time
then
n = 13 - 7 = 6 nickels
and
q = 13 + 5 = 18 quarters
You can check these values in the 1st equation
:
:
2. Grammy's change rack contained $8.80 in quarters, dimes, and nickels.
.05n + .10d + .25q = 8.80
:
There were two more than five times as many nickels as quarters
n = 5q + 2
:
and four less than twice as many dimes as quarters.
d = 2q - 4
This one in terms of q
.05(5q+2) + .10(2q-4) + .25q = 8.80
.25q + .10 + .20q - .4 + .25q = 8.80
.70q - .3 = 8.80
.70q = 8.80 + .30
.70q = 9.10
q = 9.10/.70
q = 13 quarters
You find d and n using the above equations, check the total to be 8.80
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = number of nickels
Let = number of dimes
Let = number of quarters
----------------------------------
given:
(1) ( in cents )
(2)
(3)
---------------------
This is 3 equations with 3 unknowns, so it's solvable
Substitute (3) into (1)
(1)
and
(2)
(2)
Substitute (2) into (1)
(1)
(1)
(1)
(1)
(1)
and
(3)
(3)
(3)
and
(2)
(2)
(2)
There are 6 nickels, 13 dimes, and 18 quarters
check:
(1)
(1)
(1)
OK
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