SOLUTION: A number plus half of another number equals 6; twice the first number minus three times the second number equals 4. What are the numbers?

Question 1132744: A number plus half of another number equals 6; twice the first number minus three times the second number
equals 4. What are the numbers?
Found 4 solutions by josgarithmetic, greenestamps, ikleyn, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Let these numbers be x and y.

The description means , and solving this system should not be complicated - either substitution method or elimination method.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Algebraically....

x + (1/2)y = 6
2x - 3y = 4

Double the first equation and subtract the second equation from the resulting equation; that will eliminate x and let you solve for y. Then substituting that value of y in either of the original equations lets you solve for x.

You can solve this kind of problem, if the numbers are "nice", mentally, without the formal algebra.

One of the given equations says one number plus half of another number is equal to 6. Since the fraction makes the arithmetic a bit harder, double that piece of information to find that twice the first number plus the second number is 12.

Then the two pieces of information both involve twice the first number, so comparing the two equations (that is, subtracting one equation from the other) lets you find the second number.

Then of course use that second.number with either of the original pieces of information to find the first number.

You will find the informal path to the answer is EXACTLY the same as the algebraic path, but without the need for pencil and paper.

Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

Let these numbers be x and y. The description means + = 6, (1) 2x - 3y = 4. (2) Multiply equation (1) by 2; keep equation (2) as is. You will get 2x + y = 12 (3) 2x - 3y = 4. (4) (which is the same as (2) ) Subtract equation (4) from equation (3). The terms "2x" will cancel each other, and you will get a single equation for the unknown y: y - (-3y) = 12 - 4, or 4y = 8 =================> y = 8/4 = 2. Then from equation (3) you have 2x + 2 = 12 ====> 2x = 12 - 2 = 10 ====> x = 10/2 = 5. ANSWER. x= 5; y= 2. The solution will be uncompleted until you CHECK it. Please do it on your own to make sure that my answer is correct.

In my solution, I used an elimination method, so you know now how it works.

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By the way, for your safety, ignore the solution and the answer by @josgarithmetic, since they are   W R O N G.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

A number plus half of another number equals 6; twice the first number minus three times the second number
equals 4. What are the numbers?

The 2 numbers ARE NOT . Try to solve it. You may be able to do a better job at getting the correct numbers than the 2 people who responded.
One gave you a RIDICULOUS solution and the other didn't even correct the other and give you the correct answer.
Consider this a challenge and try to get the correct answers. At least you know it's not those I stated before.
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