Solving Word Problems

[tlcourtney]

I was doing very well up until this point. :roll: Please help me...
One number exceeds another by 26. The sum of the numbers is 64. What are the numbers?

 

[Denis]

Hint: let x = low number; then x + 26 = high number.

 

[wjm11]

One number exceeds another by 26. The sum of the numbers is 64. What are the numbers?

First, name things (assign variables):

x = smaller number
y = bigger number

Now write equations that we know are true from the problem statement. We know that if we add 26 to the smaller number, it equals the bigger number:

x + 26 = y

We also know what the two numbers add up to:

x + y = 64

You now have two equations and two unknowns. That means you’re ready to solve. A simple substitution will work well in this case. Can you finish?

 

[tlcourtney]

Thanks greatly,

x+x+26=64
2x+26=64
2x=64-26
2x=38
2x=38 (I don't know how to put the underline, but I am trying to say 2x over 2 = 38 over 2)
x=19 (the smaller number)
x=45 (the larger number, 19+26=45)

Thanks, so the answer is 19, 45 :wink:

 

[mmm4444bot]

2x=38 (I don't know how to put the underline, but I am trying to say 2x over 2 = 38 over 2)

Hi Courtney:

We type a forward slash to show fractions. Also, it's VERY important (when using a slash) to put parentheses around any numerator or denominator that's more than a single object.

(2x)/2 = 38/2

'

x = 19

x = 45

Yes and no, because x has only one value, in this exercise.

x equals 19, period.

x + 26 is 45.

Or, if we started with Bill's system of equations above, we could also write y = 45.

Your final answer is correct. Good job.

Cheers,

~ Mark