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alexgriva [62]
3 years ago
12

The difference between seven times a number and three time a second number is 25. The sum of twice the first and five times the

second is 95. What are the numbers?
Mathematics
1 answer:
SpyIntel [72]3 years ago
8 0

The numbers are 10 and 15

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

Let the first number be "x"

Let the second number be "y"

<em><u>The difference between seven times a number and three time a second number is 25</u></em>

seven times the first number - three time a second number = 25

7(x) - 3(y) = 25

7x - 3y = 25 ------ eqn 1

<em><u>The sum of twice the first and five times the second is 95</u></em>

twice the first number + five times the second number = 95

2(x) + 5(y) = 95

2x + 5y = 95 ------- eqn 2

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

Multiply eqn 1 by 2

14x - 6y = 50 ----- eqn 3

Multiply eqn 2 by 7

14x + 35y = 665 ------- eqn 4

<em><u>Subtract eqn 3 from eqn 4</u></em>

14x + 35y = 665

14x - 6y = 50

( - ) --------------------

41y = 665 - 50

41y = 615

<h3>y = 15</h3>

<em><u>Substitute y = 15 in eqn 2</u></em>

2x + 5y = 95

2x + 5(15) = 95

2x + 75 = 95

2x = 95 - 75

2x = 20

<h3>x = 10</h3>

Thus the numbers are 10 and 15

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