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atroni [7]
3 years ago
8

Jennifer went on a shopping spree, spending a total of $165 on a skirt, a sweater, and a pair of shoes. The cost of the sweater

was 8/7 of the cost of the skirt. The shoes cost $11 more than the skirt. Find the cost of each item.
Mathematics
1 answer:
ahrayia [7]3 years ago
7 0
X=skirt
y=sweater
z=shoes

x+y+z=165
y=8/7x
z=x+11
plug it in
x+(8/7x)+(x+11)=165
2x+8/7x=154
22/7x=154
x=49
y=56
z=60
a skirt cost $49, a sweater cost $56, and a pair of shoes cost $60
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1. On a 20 question test, Sarah got 2 questions wrong. What percent of the test does he have correct?
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Read 2 more answers
A lab technician needs 60mL of 25% acid solution for a certain experiment , but he has only 10% solution and 40% solution. How m
V125BC [204]

Answer:

  • 10%: 30 mL
  • 40%: 30 mL

Step-by-step explanation:

The needed concentration is exactly halfway between the available concentrations, hence they must be mixed equally.

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_____

The first step in solving any problem is to look at the given information, and at what is being asked for. Here, the mix that is being asked for is exactly halfway between the given concentrations, so you know without any further contemplation that the mix will be 50%/50% of each.

__

If the mix were something else, there are several ways the problem can be solved. I like to use a diagram that puts the available concentrations on the left in a column with the highest on top, the needed concentration in the next column in the middle, and the differences of these numbers on the diagonals in the right column.

<u>Example</u>: if the needed mix is 15%, the diagram would look like ...

   40            5

          15

   10           25

The numbers on the right tell you the proportions required (5:25 = 1:5). For this example, you need 1 part 40% solution and 5 parts 10% solution to make a mix that is 15%. That's a total of 6 parts, so each "part" is 10 mL for 60 mL of solution.

We chose this example so every number in the diagram is different, so you could see how the instructions for use apply.

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Another way to solve this is to let a variable represent the amount needed of <em>the highest concentration</em>. If we let that variable be x, for the given problem, we can write the equation for the amount of acid in the mix as ...

  40%(x) + 10%(60 -x) = 25%(60)

  0.30x = 9 . . . . . . . . subtract 6, simplify

  x = 9/0.30 = 30 . . . . . mL of 40% solution

6 0
3 years ago
Please give me the correct answer.Only answer if you're very good at math.Please don't put a link to a website.Please use the Py
Angelina_Jolie [31]
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