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Please assist me with these story problems.​

Please assist me with these story problems.​-example-1

1 Answer

3 votes

Answer:

4. 16

5. $88

6. $687.50

Explanation:

4. Let n represent the number.

An expression representing the number multiplied by 0.9 and 6.3 subtracted from the product is ...

0.9n -6.3

We want that result to be 4.5, so we have the equation ...

0.9n -6.3 = 4.5

Since all of the coefficients are divisible by 0.9, we can divide by 0.9 to get ...

n -7 = 9

Adding 7 gives ...

n = 16

The number is 16.

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5. For a problem like this, I like to work it backward. If Craig got an extra $18, then everyone's share was $32 -18 = $14. That was the share from a 5-way split, so the amount the friends split evenly was 5×$14 = $70. The total they started with must have been $70 +18 = $88.

The amount they split unevenly was $88. The amount they split evenly, after setting aside $18 for Craig's parents, was $70.

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It is a bit tricky to write one equation for the amount the friends started with before they did any splits. Call that amount A. Then after setting aside $18, they split (A-18) five ways. Each of those splits was then (A-18)/5. When the $18 was added to one of those, the result was the $32 that Craig got. So, we have ...

(A -18)/5 +18 = 32

and the solution process is similar to the "working backward" description above: subtract 18, multiply by 5, add back 18.

(A -18)/5 = 14

A -18 = 70

A = 88 . . . . . . . . the amount the friends split unevenly

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6. Let P represent the original price of the laptop. We're told the price after all of the discounts was 500, so we have ...

P -50 -(0.20P) = 500

0.80P = 550 . . . . . add 50, collect terms

P = 687.50 . . . . . . . divide by the coefficient of P

The original price was $687.50.

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