What is the average of the two numbers?

In an intense session of "Space Raiders", Brian scored an even positive number of points. Tiring of this game, he switched over to "Pac-It-Up", where he scored the next larger even number.

If 1/4 of his "Space Raiders" score and 5/6 of his "Pac-It-Up" score have a sum of 32, what is the average of the two number?

There is the question. Can anyone even just help me set it up? :?:

On 'space raiders' he scored 2n points. On 'Pac it up' he scored 2n+2 points.

(1/4)(2n)+(5/6)(2n+2)=32

Since you posted this question to the "Arithmetic" category, rather than to either of the "Algebra" categories, I will assume that you haven't taken algebra yet, and don't know about variables. Here is a non-algebraic solution method:

Draw a bar (a rectangle) representing the score for the first game. Draw another bar, the same size, for the score for the second game, and write "+ 2" after this second bar.

Divide the bars into fourths with vertical lines. Then, with horizontal lines, divide the bars into thirds. These vertical and horizontal lines then divide the bars into twelve "blocks" each. This allows you to consider both "1/4" and "5/6" with respect to the bars.

Now note that 1/4 = 3/12, 5/6 = 10/12, (5/6)(2/1) = 5/3, and 32 = 96/3. Use this to create an "equation" representing the scores. It should look something like:

. . . . .3(blocks) + 10(blocks) + 5/3 = 32

Solve this for the value of a "block". Then work backwards to find the scores.

Eliz.

Actually Im taking trig so i have but i didnt understand the ? it wasnt from a class or anything it was some on-line quiz thing. I read it wrong.


but i dont get what you mean to do with the boxes. Isnt there just a basic way to do it?

xrachx08 said:

Actually Im taking trig....

Click to expand...

So you have taken algebra...? If so, then just use the algebraic set-up already provided in the first reply.

xrachx08 said:

but i dont get what you mean to do with the boxes. Isnt there just a basic way to do it?

Click to expand...

That is a "basic" way of doing it: non-algebracially. (It is the method my nine-year-old uses in his curriculum to solve this sort of exercise.) Try drawing the pictures and following the instructions to see how it works.

Or else use what you learned back in algebra to complete the solution as set up in the first reply.

Eliz.