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
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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) (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) (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 (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
Start with the second equation
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:
Multiply the both sides of the first equation by -50.
Distribute and multiply.
So we have the new system of equations:
Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
Group like terms.
Combine like terms. Notice how the x terms cancel out.
Simplify.
Divide both sides by to isolate .
Reduce.
------------------------------------------------------------------
Now go back to the first equation.
Plug in .
Multiply.
Add to both sides.
Combine like terms on the right side.
Divide both sides by to isolate .
Reduce.
So our answer is and .
This means that Will bought 3 pencils and 14 pens
Answer by scott8148(6628) (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) (Show Source): You can put this solution on YOUR website!
Remember the following,
Number of Pencils=
Number of Pens=
So, right? -----------------------------> EQN 1
In EQN 1 ,we also get,
----------------------------------------> EQN 2
Next, we know the cost for each pencil & Pen with a total cost of $5.00, so
------------------------------> EQN 3
Subst. EQN 2 in EQN 3,
-------->
, Number of Pens
Via EQN 2, , Number of Pencils
In doubt? Go back EQN 3,
Thank you,
Jojo
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