SOLUTION: I am helping my 5th grade son with his homework. I would like to give him a formula to this word problem. A pencil cost .50 and a pen cost .25. If Will spends 5 dollars on 17 pens

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I am helping my 5th grade son with his homework. I would like to give him a formula to this word problem. A pencil cost .50 and a pen cost .25. If Will spends 5 dollars on 17 pens      Log On


   

Question 163036: I am helping my 5th grade son with his homework. I would like to give him a formula to this word problem.
A pencil cost .50 and a pen cost .25. If Will spends 5 dollars on 17 pens and pencils, how many of each does he buy?
Found 4 solutions by ankor@dixie-net.com, jim_thompson5910, scott8148, jojo14344:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A pencil cost .50 and a pen cost .25. If Will spends 5 dollars on 17 pens and pencils, how many of each does he buy?
:
Let x = no. of pencils
Let y = no. of pens
:
x + y = 17
Arrange for substitution
y = (17-x)
and
.50x + .25y = 5.00
Substitute (17-x) for y and find x
.50x + .25(17-x) = 5.00
solve for x

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=# of pencils and y=# of pens

Since he bought "17 pens and pencils", this means that the first equation is x%2By=17 (ie the sum of the two items is 17)

To find the second equation, this formula will help:

Price per pencil* Number of pencils + Price per pen * Number of pens = Total cost

Since the price per pencil is 0.50 and the price per pen is $0.25, and the total cost is $5, this means that the second equation is 0.50x%2B0.25y=5


0.50x%2B0.25y=5 Start with the second equation


50x%2B25y=500 Multiply EVERY term by 100 to move the decimal point two spots to the right. This will make every number a whole number.


So we have the system of equations:
system%28x%2By=17%2C50x%2B25y=500%29


-50%28x%2By%29=-50%2817%29 Multiply the both sides of the first equation by -50.


-50x-50y=-850 Distribute and multiply.


So we have the new system of equations:
system%28-50x-50y=-850%2C50x%2B25y=500%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-50x-50y%29%2B%2850x%2B25y%29=%28-850%29%2B%28500%29


%28-50x%2B50x%29%2B%28-50y%2B25y%29=-850%2B500 Group like terms.


0x%2B-25y=-350 Combine like terms. Notice how the x terms cancel out.


-25y=-350 Simplify.


y=%28-350%29%2F%28-25%29 Divide both sides by -25 to isolate y.


y=14 Reduce.


------------------------------------------------------------------


-50x-50y=-850 Now go back to the first equation.


-50x-50%2814%29=-850 Plug in y=14.


-50x-700=-850 Multiply.


-50x=-850%2B700 Add 700 to both sides.


-50x=-150 Combine like terms on the right side.


x=%28-150%29%2F%28-50%29 Divide both sides by -50 to isolate x.


x=3 Reduce.


So our answer is x=3 and y=14.

This means that Will bought 3 pencils and 14 pens

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x="number of pencils", so 17-x="number of pens" (pens plus pencils is 17)

x(.50)+(17-x)(.25)=5.00 __ .50x+4.25-.25x=5.00 __ .25x=.75 __ x=3 __ 17-x=14

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Remember the following,
Number of Pencils=x
Number of Pens=y
So, x%2By=17 right? -----------------------------> EQN 1
In EQN 1 ,we also get,
x=17-y ----------------------------------------> EQN 2
Next, we know the cost for each pencil & Pen with a total cost of $5.00, so
0.50x%2B0.25y=5.00 ------------------------------> EQN 3
Subst. EQN 2 in EQN 3,
0.50%2817-y%29%2B0.25y=5.00
8.5-0.50y%2B0.25y=5.00
8.5-5.00=0.50y.25y
3.50=0.25y --------> cross%283.50%2914%2Fcross%28.25%29=cross%280.25%29y%2Fcross%280.25%29
highlight%28y=14%29, Number of Pens
Via EQN 2, highlight%28x=17-14=3%29, Number of Pencils
In doubt? Go back EQN 3,
0.50%283%29%2B0.25%2814%29=5.00
1.50%2B3.50=5.00
5.00=5.00
Thank you,
Jojo