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QThere are two numbers such that 4 times the smaller one is less than 3 times the larger one by 5, and the sum of the numbers is larger than 6 times their difference by 6. Determine the values of these numbers

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#4480Q ID
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  • A 59, 43 ✔ ✖
  • B 45, 34 ✔ ✖
  • C 87,56 ✔ ✖
  • D 39, 45 ✔ ✖
Correct Answer

Explanation

Given:

4 times the smaller of two numbers is less than 3 times the larger number by 5
The sum of the two numbers is larger than 6 times their difference by 6
Let the two numbers be x and y, such that x > y. 
Then the given conditions can be expressed as the following equations:

3x - 4y = 5
(x + y) - 6 (x - y) = 6
Solve these equations simultaneously to find the values of x and y:

(x + y) - 6 (x - y) = 6
-5x + 7y = 6
Solve for x:

x = 59
Substitute this value for x into the first equation to solve for y:

3(59) - 4y = 5
177 - 4y = 5
4y = 172
y = 43
Therefore, the two numbers are x = 59 and y = 43.

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