Question

Twice a number plus twice a second number is 310. The difference between the numbers is 55

Answer 1

The problem involves setting up two simultaneous equations to solve for two unknowns. Using the elimination method, we can determine that the first number is 105 and the second is 50.

Step-by-step explanation:

To help the student, we need to set up two equations based on the information given:

1. Let the first number be x and the second number be y.
2. The equation from the first sentence is: 2x + 2y = 310.
3. The equation from the second sentence is x - y = 55.
4. Solve these equations simultaneously to find the values of x and y.

Multiply the second equation by 2 to aid in the elimination method, which results in the equation 2x - 2y = 110.

Adding this to the first equation,

2x + 2y = 310
+

2x - 2y = 110
---------------

4x = 420

Divide by 4 to solve for x:

4x / 4 = 420 / 4

x = 105

To find y, substitute x into the second original equation:

x - y = 55

105 - y = 55

y = 105 - 55

y = 50

Therefore, the two numbers are 105 and 50.

Answer 2

x = 105

y = 50

Step-by-step explanation:

To solve this, try writing it out as an equation/expression first.

When you do, you should get something like this:

2x + 2y = 310

x - y = 55

This is a system of equations. To solve this, we're going to multiply the second equation [x - y = 55] by 2.

2(x - y = 55) = 2x - 2y = 110

Now, subtract your new equation from the first one [2x + 2y = 310]

2x + 2y = 310

-2x + 2y = -110

//If you're wondering why I changed the signs of the new equation, I multiplied our new equation [2x - 2y = 110] by -1 since we're subtracting//

When you're done subtracting, the "2x" and "-2x" cancel out, so you're left with:

4y = 200

Now, simply solve for "y" by dividing both sides by 4.

4y = 200

y = 50

Now that we know y's value, substitute it into one of our original equations to solve for x.

//I'm gonna plug y into the second equation [x - y = 55] just because it's easier, but you can plug it into the first one as well and get the same answer//

When we plug it in, we get:

x - (50) = 55

To solve for "x," we must get rid of "-50." To do this, add 50 to both sides.

x - 50 = 55

x = 105

So, x = 105 and y = 50