SOLUTION: Hi Mrs Lee went shopping with a certain amount of money. If she wanted to buy 15 shirts she would need another $150. If she bought 5 shirts she would have $250 left. How much did

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Question 1205896: Hi
Mrs Lee went shopping with a certain amount of money. If she wanted to buy 15 shirts she would need another $150. If she bought 5 shirts she would have $250 left. How much did a shirt cost.
Found 4 solutions by mananth, greenestamps, josgarithmetic, MathTherapy:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Mrs Lee went shopping with a certain amount of money. If she wanted to buy 15 shirts she would need another $150. If she bought 5 shirts she would have $250 left. How much did a shirt cost.
Let Mrs. Lee have $ x with her when she went shopping
When she wants to buy 15 shirts she feels short of $150
Total cost of 15 shirts = x+150
Cost of each shirt will be (x+150)/15
If she bought 5 shirts amount left with her is 150
5*(x+150)/15 + 250 = x
(x+150)/3 = x-250
x+150 = 3(x-250)
x+150 = 3x -750
Rearrange and simplify
3x-x = 150+750
2x = 900
x =450
She had $450
Let cost of shirt be y
15y = 450+150
15y = 600
y= 40
Cost of each shirt = $40
I have corrected this problem. Thanks to my fellow tutor.

Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


There is an error in the work shown by the other tutor, which she could have found if she had checked to see if her answer satisfies the given conditions.

Note that the error in her work was easy to make because of the awkward way she chose to set up and solve the problem.

Informally, the difference between 15 shirts and 5 shirts is 10 shirts; the difference between being $150 short and having $250 left is $400. That means the cost per shirt is $400/10 = $40.

Formally....

let x be the cost of each shirt

The amount of money Mrs Lee had was $150 less than the cost of 15 shirts: 15x-150.

The amount of money she had was $250 more than the cost of 5 shirts: 5x+250.

Solve the equation that says those two expressions for the amount Mrs. Lee had are equivalent:

15x-150 = 5x+250
10x = 400
x = 40

ANSWER: The cost of each shirt was $40

Presumably the formal algebraic solution was what the student was looking for. Note, however, that the path to the answer using formal algebra is identical to the informal path.

The student should understand the formal solution; but being able to solve the problem informally using logical reasoning is a valuable skill.
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
M, Lee's amount of money with went shopping
p, price of shirt

Bought the 15 shirts


Bought just 5 shirts


Find p, the price of 1 shirt.


prepare substitution for M.

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Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
Hi
Mrs Lee went shopping with a certain amount of money. If she wanted to buy 15 shirts she would need another $150. If she bought 5 shirts she would have $250 left.  How much did a shirt cost.

Let cost of a shirt be S
Since purchasing 15 shirts would've required an additional $150, amount she had, was 15S - 150
And, since purchasing 5 shirts would've left her with $250, amount she had, was 5S + 250
We now set the 2 expressions equal to each other, as follows:  15S - 150 = 5S + 250
                                                                15S - 5S = 250 + 150
                                                                     10S = 400
                                                  Cost of a shirt, or

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