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soldi70 [24.7K]
2 years ago
12

The sum of two numbers is 5, and the difference between the first number and twice the second number is 29.

Mathematics
1 answer:
aivan3 [116]2 years ago
3 0
<h2>Converting Words into Equations</h2>

We can convert word problems into equations by translating key terms into operations:

  • <em>sum</em> = we add
  • <em>difference</em> = we subtract
  • <em>twice</em> = multiply by 2
  • <em>is</em> = equals

<h2>Solving the Question</h2>

We're given:

  • sum of two numbers is 5
  • difference between the first number and twice the second number is 29

Let the first number be <em>a</em> and the second number be <em>b.</em>

Translate the words into numbers:

  • <u>sum</u> of two numbers <u>is</u> 5
    a+b=5
  • <u>difference</u> between the first number and <u>twice</u> the second number <u>is</u> 29
    a-2b=29

Subtract the second equation from the first to isolate <em>b</em>:

(a+b)-(a-2b)\\=a+b-a+2b\\=b+2b\\=3b

5-29\\=-24

3b=-24\\b=-8

Therefore <em>b</em> is -8.

Substitute <em>b</em> back into the first equation to find <em>a</em>:

a+b=5\\a-8=5\\a=13

Therefore, <em>a</em> is 13.

<h2>Answer</h2>

<em>a</em> = 13

<em>b</em> = -8

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