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Sally is going to buy a total of 11 new items at Target. She is going to buy jeans, dresses, and
shoes. She is going to spend exactly $460 and has discovered that jeans are $25, dresses are $50,
and shoes are $40. She is also going to buy twice as many shoes as jeans. Find out how many
jeans, how many shoes, and how many dresses she will buy?
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Let x = the unknown number of jeans, and
let y = the unknown number of dresses.
Then the unknown number of shoes is 2x, according to the condition.
Now we can write our equations, TWO equations in TWO unknowns:
x + 2x + y = 11, (1) (counting for items)
25x + 40*(2x) + 50y = 460. (2) (counting dollars of spending)
Simplify the system:
3x + y = 11, (3)
105x + 50y = 460. (4)
To solve the system, I will apply the substitution method.
For it, express y = 11-3x from (3) and substitute it into eq(4). You will get
105x + 50*(11-3x) = 460 ====>
105x + 550 - 150x = 460 ====> -45x = 460 - 550 = -90 ====> x = = 2.
Thus we found the unknown x. It is x= 2.
Then from eq(3) y = 11 - 3x = 11- 3*2 = 11-6 = 5.
Answer. 2 jeans, 2*2 = 4 shoes and 5 dresses.
Check. 2*25 + 4*40 + 5*50 = 460. ! Correct !
Solved.
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The lesson to learn from this solution:
This problem is for 2 unknown.
It is not for 3 unknowns, as you may think at the first glance.
Solving with 2 unknowns is much easier than with 3 unknowns.
Therefore I made all the efforts required to solve it with 2 unknowns, not with 3.