Algebra Question

Question

Mairé is thinking of two numbers. The first number is 14 less than the second number. When she adds them, she gets 40. Find the two numbers.

Answer 1

Hello Lynleigh, There are two ways to solve this: with one variable or with two variables. With two variables, you would have x = y - 14 and x + y = 40. See if you can solve this system.

OR If you want to use one variable, see if you can write the problem using just y where the two numbers are y and y - 14.

Tom S.

Answer 2

Hi Lyneigh,

For this example we are going to assign the two numbers Maire is thinking of to variables x and y.

The first number is 14 less than the second number.

x= y-14

When she adds them, she gets 40

x+y=40

Use the above solution for X to fill in the equation

y-14+y=40

2y-14=40

+14 +14

2y=54

/2 /2

y=27

Solve for x

x= y-14

x= 27-14

x=13

Check

x+y=40

13+27=40

Answer 3

Since the two numbers add up to 40, I would start by splitting 40 in half to get 20 and 20.

Then, I would take the difference between the two numbers (14), and split that in half to get 7.

Now, if I subtract 7 from 20 to get 13 for one number, and I add 7 to 20 to get 27 for the 2nd number, then the difference between the two numbers will be 14 because 27-13 =14.

Now, check that 13 + 27 =40.

That checks out; so, the two numbers are 13 and 27.

You can set this up algebraically by saying that your two numbers are x and y.

Then, the sum of them is 40. Therefore, x + y =40

You also are told that the 1st number is 14 less than the 2nd number. Therefore, y - x =14.

This gives you two equations and two unknowns. We can then solve an equation for one variable and substitute that into the other.

So, I can take y - x =14 and add x to both sides to get y = 14 + x

Now that I have solved that equation for y, I can use substitution and plug that value of y into the other equation.

So we have x + y =40, and we have y = 14 + x.

Therefore, substituting for y into the first equation gives us x + 14 + x = 40.

Combine like terms to get 2x + 14 =40

subtract 14 from each side to get 2x = 26.

divide both sides by 2 to solve for x, which is x = 13

Now that you know the value of x, you can plug it into the other equation y -x =14 to get

y - 13 =14

Now solve that for y by adding 13 to each side, and you get y = 27.

You know have determined the values of the two numbers.

Answer 4

So first we want to set up an equation with the information provided to us.

We know we have two numbers (X & Y). In this case, x is our first number and y is our second number.

Step 1-

1. We know the first number is 14 less than the second number. To write this equation we will have something like this: X= Y-14

Step 2-

1. Then we know that the sum of both of these numbers is 40. So we will add these numbers together and set them equal to 40: X+Y=40

Step 3-

1. To solve, we will plug the first equation into the "X" of the second equation because we know X is y-14. This would look like this: (y-14)+y=40
2. Then we want to solve for Y
3. 2y-14=40 (add the Y from outside the parenthesis to the Y on the inside of the parenthesis)
4. 2y=54 (subtract 14 from each side of the equation)
5. y=27 (divide each side of the equation by 2)

Step 4-

1. Now that we know what Y equals we are able to go back to our original equations and plug this number in to find the second number for our question.
2. x=y-14 (original equation)
3. x=27-14
4. x=13

Answer: 13 and 27 are the two numbers thought of.

I hope this helps!

Answer 5

You can represent this problem with 2 equations. If we call the numbers x and y, we know that:

x + y = 40

and

y - 14 = x (because x, the first number, is 14 less than y)

We can solve this several ways, but the easiest is substitution. Substitute "y-14" for "x" in the first equation because "y-14" is equivalent to x.

That gives us y - 14 + y = 40. Now that we only have one unknown, we can solve easily.

Then combine the y and y to get 2y: 2y - 14 = 40

Add 14 to both sides: 2y = 54

Divide both sides by 2: y = 27.

By the rules stated in the question, x must be 13!

We can also solve this problem intuitively by taking a guess at a reasonable value for y and adjusting until we're correct. If y is 14 more than x, and together the two equal 40, maybe y is 25? That would make x=11 (14 less than y), and 25+11 is only 36. Obviously y needs to be a little larger. If we try 27, we find that is the right answer.