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.