Word Problem, Computing grades

[BaldLilFairy]

The problem reads:
Going into the final exam, which counts as three grades, Mark has test scores of 65, 78, 64, and 88. What score does mark need on the final exam in order to have an average of 70?

I know to find the average you add up all your grades and divide the answer by the number of test but, I am just not getting how to write the equation for this. Everything I try gets me the wrong answer. I know the answer is Mark needs to get a 65 on his final exam.

Do I add the number of test he has taken and divide by 7? by 5? is the variable 3X or just X?
I can find examples of all the other word problems located in the chapter but nothing for computing grades and I have 4 other problems along the same lines to answer.

 

[Denis]

(65 + 78 + 64 + 88 + 3x) / 7 = 70
295 + 3x = 490
3x = 195
x = 65
WHY were you not getting that?

 

[BaldLilFairy]

Maybe because I was foolishly not multipling the 70 on the right by 7. It didn't occur to me. I noticed that when you work a problem for a long time you get wrapped up in the wrong order of operation. Please excuse me for asking what you feel was a silly question. I thank you for your response.

 

[Denis]

I noticed that when you work a problem for a long time you get wrapped up in the wrong order of operation.

YEP! Been there, done that

 

[CrystalPlus5]

I DO NOT think it was a silly ques!! Thanks for asking... it helped me a lot w/ a similar problem... now I just have to remember how I know to multiply the 7 by 70.... I know it must be a property of some but I don't recall Thanks again!

(65 + 78 + 64 + 88 + 3x) / 7 = 70
295 + 3x = 490
3x = 195
x = 65
WHY were you not getting that?

 

[mmm4444bot]

I just have to remember how I know to multiply the 7 by 70.... I know it must be a property of some but I don't recall

Both sides of the equation must be multiplied by 7, not just 70.

Multiplying the lefthand side of the equation by 7 eliminates the fraction.

There is no property for this, but, if there were, it might be called something like the "As long as x remains in the numerator of a fraction, you cannot solve for x" property. :cool:

 

[Deleted member 4993]

I DO NOT think it was a silly ques!! Thanks for asking... it helped me a lot w/ a similar problem... now I just have to remember how I know to multiply the 7 by 70.... I know it must be a property of some but I don't recall Thanks again!

It helps to multiply both sides by 7 - you get rid of fractions (Denis - well most of us - hate/s to work with fractions)

If you don't do that then you'll have:

(65 + 78 + 64 + 88 + 3x) / 7 = 70

65/7 + 78/7 + 64/7 + 88/7 + 3x/7 = 70

3x/7 = 70 - 65/7 - 78/7 - 64/7 - 88/7

3x/7 = see what a mess it got into.....