the sum of two numbers is 11 and the difference is 5

Question

I need to know what it is for this practice im doing at home. my teacher said i could use this site for help.

Answer 1

Word problems are easier if you just write down EXACTLY what they say. You need to know math vocabulary, however, - and that is VERY IMPORTANT.

SUM - means the answer to an addition problem.

DIFFERENCE - means the answer to a subtraction problem.

(If you don't know them, look up product and quotient - you will need to know those too for the test.)

So, for your problem - "the sum of 2 numbers is 11". I don't know what they 2 numbers are..., and the question probably goes on to ask you what they are. So I will call them x and y, and once I solve for x and y, I will have my answer.

If the SUM of x and y IS 11 --- take note that IS is also a math word - it represents =.

We can simply "translate" these words "into math":

x + y = 11.

Can you set up an equation for the DIFFERENCE? You will now have a second equation.

Once you do that, you will have 2 equations and 2 unknowns, x and y. For a test like Accuplacer, you can use substitution or elimination to solve.

Substitution can sometimes be tedious, but in this case, it is not Let's use the SUM equation to solve for x - you do that by simply rearranging the equation:

x + y = 11

subtract y from both sides:

x = 11 - y.

Now you have a second equation from the difference -

You should have gotten x - y = 5.

Let's substitute for that x in the beginning of this equation:

x - y = 5.

(11-y) -y = 5

combine like terms:

11 - 2y = 5

add 2y to both sides of the equation,

then subtract 5 from both sides of the equation, and hopefully you can take it from there to solve for y.

But that is only 1 of the numbers. Use one of your equations to solve x, given the value of y you found.

Now CHECK - is the SUM 11? Is the DIFFERENCE 5?

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Knowing how to USE MATH VOCABULARY to simply write down what is being given in the question is the KEY to solving word problems.

REVIEW substitution and ELIMINATION (another method not discussed here), to solve "systems of equations" (which is a fancy way of saying "more than one equation"). Accuplacer will expect you to know these skills.

All the best!