Dave J. answered • 10/28/15

Experienced Analyst and Expert User - MS Office, Excel, Access and VBA

Junior R.

asked • 10/28/15 The sum of two numbers is 57 and the difference is 7. What are the numbers? What is the large #?

What is the smaller#?

What is the smaller#?

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Dave J. answered • 10/28/15

Experienced Analyst and Expert User - MS Office, Excel, Access and VBA

You can write 2 equations that meet the criteria:

The sum of two numbers is 57

x + y = 57

The difference is 7

x - y = 7

Solve the second equation for x, and substitute in the first equation to solve for y

- solve the second equation for x.

Add y to both sides of the equation

x - y + y = 7 + y

x = 7 + y

- substitute x = 7 + y into the first equation

x + y = 57

(7 + y) + y = 57

7 + 2y = 57

Subtract 7 from both sides of the equation

7 - 7 + 2y = 57 - 7

2y = 50

Divide both sides of the equation by 2 to solve for y

y=25

Insert y = 25 into either equation and solve for x

x - y = 7

x - 25 = 7

Add 25 to both sides of the equation

x - 25 + 25 = 7 + 25

x = 32

Answer: x = 32, y = 25

As a check, plug these values into both equations to make sure that it works

Nayoon K. answered • 10/28/15

MIT Tutor Specializing in Math / Science / Test Prep

Haha. This is a fun question. Let's call the large # L and the smaller # S. We can now express the sentences in math equations.

The sum of two numbers is 57 becomes L+S=57. The difference is 7 becomes L-S=7. Therefore, we now have two math equations:

L+S=57 (equation 1)

L- S= 7 (equation 2)

Now, we can add these two equations.

L+S=57

L- S= 7

L- S= 7

2L = 64

Dividing by 2 on each side,

2L = 64

2 2

L=32

We can now use the substitution of L=32 to L+S=57.

L+S=57

32+S=57

S=57-32=25.

Yay! The larger number is 32 while the smaller number is 25. Check the second equation to see if this works:

L-S=7

32-25=7? Yes! Therefore, this answer is correct.

Don L. answered • 10/28/15

Fifteen years teaching and tutoring basic math skills and algebra

Hi Junior, let the two numbers be x and y. We can now create to equations to solve for the x and y.

x + y = 57

x - y = 7

Add the two equations together giving:

x + y = 57

x - y = 7

-------------

2x = 64

Divide both sides by 2 to find x.

x = 32

Substitute for x in the first equation.

32 + y = 57

Subtract 32 from both sides to find y.

y = 25

The two numbers are 32 and 25, with the larger number being 32.

Questions?

Alexander B. answered • 10/28/15

PhD in Engineering with 20 yrs of Math and Science Teaching Experience

Solve the following system of linear equations:

X+Y=57

X-Y=7

the answer is: X=32, Y=25

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