The Difference Of Two Numbers Is 17. Find The Numbers If Twice The Smaller Plus Three Times The Larger Is 66.
The difference of two numbers is 17. Find the numbers if twice the smaller plus three times the larger is 66.
Number Problems:
Answer:
The two numbers are 20 and 3.
Step-by-step explanation:
To find for the two numbers, let x be the larger number and y be the smaller number then x - y = 17 and 3x + 2y = 66. In order to apply the elimination method, multiply x - y = 17 by 2 such that 2(x - y = 17) which will give 2x - 2y = 34. Add 2x - 2y = 34 to 3x + 2y = 66 to eliminate y and solve for x such that 2x + 3x = 5x, -2y + 2y = 0, 34 + 66 = 100 then 5x = 100. Divide both sides of the equation by 5 thus, x = 20. If the larger number is 20 then use x - y = 17 such that 20 - y = 17, -y = 17 - 20, -y = -3. To remove the negative sign of y multiply both sides of the equation by -1 such that -1(-y = -3) thus, y = 3. To check whether the obtained numbers are correct, use x - y = 17 then 20 - 3 = 17, 17 = 17 or 3x + 2y = 66, 3(20) + 2(3) = 66, 60 + 6 = 66, 66 = 66.
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