Substitution?

Question

For algebra I have a word problem and i need to figure out the equations "The first number is 12 less than the second number. Twice the first number increased by the second is 26. Find the numbers" How would I figure that out? I dont just want the answer, I want help. Thanks

Answer 1

call the 1st number: x-12
call the 2nd number: x

then apply the word problem to your two numbers:

is means =
twice the first... multiply the first. increased by the second... add the second # to what you just did:

2(x-12) + x = 26

then solve for x. REMEMBER: you assigned the 2nd number as x. so, you have just found the second number. To find the first number, look at your above equation. the 1st number is x-12, so subtract 12 from x and you have the first number.


hope this helped! =]

Answer 2

Write the words in math form:

NumberOne = NumberTwo - 12
2 * NumberOne + NumberTwo = 26

Since this problem is supposed to be done by substitution and the first statement is pretty simple, we'll just substitute Statement 1 into Statement 2:

2*(NumberTwo - 12) + NumberTwo = 26

Now you have an expression with only one variable and you can solve it:

3*NumberTwo = 50

NumberTwo = 50/3

Now substitute this result back into the first statement:

NumberOne = 50/3 - 12 = 50/3 - 36/3
NumberOne = 14/3

Check:
2*14/3 + 50/3 = 26
28/3 + 50/3 =26
78/3 = 26
26 = 26
Check!