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Type the correct answer in each box. The sum of a number and two times a smaller number is 62. Three times the bigger number exceeds the smaller number by 116. The bigger number is ___ The smaller number is ___

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Answer:

Bigger number = 42

Smaller number = 10

Step-by-step explanation:

Step 1: Define variables

x = larger number

y = smaller number

Step 2: Write systems of equations

x + 2y = 62

3x = y + 116

Step 3: Rewrite 1st equation

x = 62 - 2y

Step 4: Substitution

3(62 - 2y) = y + 116

186 - 6y = y + 116

186 = 7y + 116

70 = 7y

y = 10

Step 5: Plug in y to find x

x + 2(10) = 62

x + 20 = 62

x = 42

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