Converting Words into Equations
We can convert word problems into equations by translating key terms into operations:
- sum = we add
- difference = we subtract
- twice = multiply by 2
- is = equals
Solving the Question
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 a and the second number be b.
Translate the words into numbers:
- sum of two numbers is 5
[tex]a+b=5[/tex] - difference between the first number and twice the second number is 29
[tex]a-2b=29[/tex]
Subtract the second equation from the first to isolate b:
[tex](a+b)-(a-2b)\\=a+b-a+2b\\=b+2b\\=3b[/tex]
[tex]5-29\\=-24[/tex]
[tex]3b=-24\\b=-8[/tex]
Therefore b is -8.
Substitute b back into the first equation to find a:
[tex]a+b=5\\a-8=5\\a=13[/tex]
Therefore, a is 13.
Answer
a = 13
b = -8
