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Home Q & A Board Science-Related Homework Help Mathematics
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mike305 mike305
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Posts: 18
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11 years ago
If the sum of two numbers is 42 and the difference is 12, then what is the product of the numbers?  (Hint: First solve for the numbers.)
[A]  216      343     [C]  405     [D]  441
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wrote...
#1
11 years ago
x+y = 42
x-y = 12 Add
2x = 54
x = 27 and y = 15
xy = 405
Answer C
wrote...
#2
11 years ago
15 and 27
15 x 27 = 405
C
wrote...
#3
11 years ago
Let the 2 numbers be x and y

x + y = 42

x - y = 12

Eliminating x's by subtraction gives

2y = 30

y = 15

x = 27

So, 27 x 15 = 405

Answer [C] 405

:-)
wrote...
#4
11 years ago
Let x and y be the 'two numbers'

x + y = 42

x - y = 12

Rearrange x + y =42 them to make y the subject,

y = 42 - x

Now substitute it in the other equation: x - y = 12

You get:

x - (42 -x) = 12

Simplify:

x - 42 +x = 12

2x - 42 = 12

Add 42 to both sides:

2x = 54

Divide both sides by 2:

x = 27

Now you know one of the numbers, it is 27, to find y, then substitute 27 for x in the equation: x - y = 12:

27 - y = 12

Subtract 27 from both sides:

-y = -15

Multiply both sides by -1

y = 15

Now you have the two numbers, they are 15 and 27, all you have to do now is multiply them:

15*27

= 405

So the answer is C
Answer accepted by topic starter
rivertuberivertube
wrote...
#5
Posts: 147
Rep: 3 0
11 years ago
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