larger is 5 more than smaller; smaller plus 2X larger is 100

[tyler]

I am in an Academic intervention class and having probs with word problems. please help.

1. the larger of two numbers is 5 more than the smaller. The smaller number plus twice the larger equals 100. find the numbers.

I have written all the numbers out but I can't figure out how to list the numbers to solve for each of the 2 numbs.

I know I have to use X for each number So the 5x would be the larger number and x would be the smaller, I get confused when it says that the smaller number plus ttwice the larger = 100. Would that be x + 2(5x) ? HELP please

 

[stapel]

1. the larger of two numbers is 5 more than the smaller. The smaller number plus twice the larger equals 100. find the numbers.

...So the 5x would be the larger number and x would be the smaller...

Does the exercise say that the larger number is five times the size of the smaller, or that it is just five units more than the other?

Eliz.

 

[Shutterbug424]

Re: word probelm help

I am in an Academic intervention class and having probs with word problems. please help.

1. the larger of two numbers is 5 more than the smaller. The smaller number plus twice the larger equals 100. find the numbers.

I have written all the numbers out but I can't figure out how to list the numbers to solve for each of the 2 numbs.

I know I have to use X for each number So the 5x would be the larger number and x would be the smaller, I get confused when it says that the smaller number plus ttwice the larger = 100. Would that be x + 2(5x) ? HELP please

Ok, you know you have two numbers to find. You also know that you don't know what the two numbers are, so you know you need to assign variables to those numbers. I would use L for the larger number and S for the smaller number.

Using those new variables try to set up the two equations they give you in the problem.

But then you'll have two separate equations with 2 different unknowns. The key is to isolate one of the variables in one problem, and substitute it into the second problem. This way you only have one unknown. Solve for that. Then use that answer to find the other unknown.

I know it sounds a little confusing, but try to set up the two equations first. I'll help you if you're still stuck.

 

[tyler]

Re: word probelm help

thanks,

I think I got the 2 equations

S + 5 = L
S+ 2L=100

2L(S+5)= 100

is that right

 

[Shutterbug424]

Re: word probelm help

thanks,

I think I got the 2 equations

S + 5 = L
S+ 2L=100

2L(S+5)= 100

is that right

The first two equations are perfect. I don't really understand the third one.

According to your first equation, L = S + 5. So, you can substitute that into the second equation to give you S + 2(S+5) = 100. Then solve for S. Then plug that value for S into your first equation to get L.

 

[tyler]

Re: word probelm help

do you think both the nos. I am looking for can be labeled with the variable x. We havent learned how to use to different variables yet, like L and S. I used those b/c you suggested it was easier to work with that way.

Thaks for the help!!!!

 

[mmm4444bot]

Re: word probelm help

...

S + 5 = L

S+ 2L=100

2L(S+5)= 100

...

The third equation is wrong; you did not properly substitute the expression for L (as defined in the first equation) into the second equation.

Your third equation -- as you've typed it -- represents the following statement, which is clearly wrong.

"Two times the larger number times the larger number equals 100."

If you replace the symbol L in your second equation with the proper expression for L, then you will get an equation that contains only the symbol S, for which you can solve.

Once you know the value of S, then use your first equation to calculate the value of L.

Cheers,

~ Mark

 

[Shutterbug424]

Re: word probelm help

do you think both the nos. I am looking for can be labeled with the variable x. We havent learned how to use to different variables yet, like L and S. I used those b/c you suggested it was easier to work with that way.

Thaks for the help!!!!

You could change the variables to x and y. Then substitute in the equation so you would only have x's.

 

[mmm4444bot]

Re: word probelm help

...

do you think both the nos. I am looking for can be labeled with the variable x.

...

NO. These two numbers are different.

The symbol x can only represent one of the constants in this exercise. We can never use a single symbol to represent two different values at once!

You could do the following, if you're trying to work this exercise using only one symbol.

Let x = the smaller number

Let x + 5 = the larger number

Cheers,

~ Mark