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 exc eeds the smaller number by 116. The bigger number is ___ The smaller number is ___
1 answer:
Answer:
Bigger number = 42
Smaller number = 10
Step-by-step explanation:
Step 1: Define variables
<em>x</em> = larger number
<em>y</em> = 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 <em>y</em> to find <em>x</em>
x + 2(10) = 62
x + 20 = 62
x = 42
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