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sweet-ann [11.9K]
2 years ago
12

The sum of two numbers is 9. And the sum of their reciprocals is 1/2.find the numbers

Mathematics
1 answer:
Musya8 [376]2 years ago
7 0
Set up a system of equations:

x + y = 9
1/x +1/y = 1/2

The easiest way to solve would be substitution.
x + y = 9 can be solved for y:

y = 9 - x

Then plug this into the second equation and solve for x:

1/x + 1/(9-x) = 1/2
(9-x) + x = x(9-x)/2
9 = (9x-x²)2
18 = 9x - x²
x² - 9x + 18 = 0
(x-6)(x-3) = 0
x = 6, 3

You can check your answer by plugging the two numbers back into both of the equations:

6 + 3 = 9
1/6 + 1/3 = 1/2

The two numbers are 6 and 3.
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A company has to buy computers and printers. Each computer, x, costs $585 and each printer, y, costs $385. If the company spends
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The company bought 9 computers and 6 printers

<em><u>Solution:</u></em>

Let "x" be the number of computers bought

Let "y" be the number of printers bought

cost of 1 computer = $ 585

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<em><u>The company buys a total of 15 machines</u></em>

Therefore, we can frame a equation as:

number of computers bought + number of printers bought = 15

x + y = 15 ------ eqn 1

<em><u>The company spends $7,575</u></em>

Therefore, we can frame a equation as:

number of computers bought x cost of 1 computer + number of printers bought x cost of 1 printer = 7575

x \times 585 + y \times 385 = 7575

585x + 385y = 7575 ------ eqn 1

<em><u>Let us solve eqn 1 and eqn 2</u></em>

From eqn 1,

x = 15 - y --------- eqn 3

<em><u>Substitute eqn 3 in eqn 2</u></em>

585(15 - y) + 385y = 7575

8775 - 585y + 385y = 7575

-200y = 7575 - 8775

-200y = -1200

y = 6

<em><u>Substitute y = 6 in eqn 3</u></em>

x = 15 - 6

x = 9

Thus the company bought 9 computers and 6 printers

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