The larger of two numbers is 2 more than three times the smaller number. The difference between the numbers is 12. Find the numbers,

Answer 1

From the information in the word problem we are able to set up the following inequality:

3y + 2 - y = 12 | where x is the larger number of two numbers in a set (x, y)

We know this because the problem states that [x = 3y + 2] or 3 times the smaller number plus two.

We also know that x - y = 12.

So, we substitute x in [x - y = 12] with 3y + 2 that we found out above, and we get the following:

3y + 2 - y = 12

Now, we solve the inequality

3y + 2 - y = 12

-> subtract 2 from both sides :: 3y - y = 10

-> subtract y from 3y :: 2y = 10

-> divide both sides by 2 :: y = 5

So now we have y, the smaller number, which is equal to 5. Next, to find x we simply plug y=5 back in to either the value of x, [3y + 2], or the inequality of x - y = 12. I will show both:

x - y = 12

-> substitute y for 5 :: x - 5 = 12

-> add 5 to both sides :: x = 17

OR

3y + 2 = x

-> substitute y with 5 :: 3(5) + 2 = x

-> multiply 3, 5 :: 15 + 2 = x

-> add 15, 2 :: 17 = x

So there you have it:

x = 17 , y = 5

You can go back and use these values to check your answer and make sure they work with the word problem.

Remember to look for the setup to an inequality in the word problem. Anything that says BLANK times this number, or 4 less than that number, is trying to set you up with an inequality problem.

I hope this helped :)

Answer 2

The larger of two numbers is 2 more than three times the smaller number. The difference between the numbers is 12. Find the numbers:

First we should define the terms,

the larger number=L, the smaller number=s

Then we convert the word problem into a system of equations:

L=2+3s

L-s=12

We plug in the first equation into the second, since we know what L is in relation to s:

(2+3s)-s=12

2+2s=12

2-2+2s=12-2

2s=10

s=5

We now know s=5. To find the larger number, we plug it into one of the equations:

L=2+3(5)

L=17

or

L-5=12

L=17

Answer 3

Nathalia,

Lets try to break up the problem.

L = larger number

S = smaller number

The larger of two numbers is 2 more than three times the smaller number. 

L = 2 + 3S

The difference between the numbers is 12.

L - S = 12

Now we can use substitution.

We will substitute L for 2+3S into the equation L-S=12

L - S = 12

2+3S - S = 12

2 + 2S = 12

2S = 10

S = 5

Now we can substiute S = 5 into one of the equations.

L - S = 12

L - 5 = 12

L = 17

Answer:

larger number = 17

smaller number = 5

I hope this helps.

Please feel free to reach me if you still need any clarification.

Thanks,

Richmond

Answer 4

Let x = the smaller number

Let 3x + 2 = the larger number

3x + 2 - x = 12

2x = 10

x = 5