Problem solving?!

Question

Suppose in a class you have test grades of 65 and 73, an 85 on the paper, and a homework grade of 40. [Assume: the three tests are worth 70%, the homework 20% and the paper 10%] What grade must you get on the third test to get a semester average of 70?

Answer 1

Set x = score of the Third Test

 

(x+65+73)/3*0.7+85*0.1+40*0.2=70

 

(x+65+73)/3*0.7+8.5+8=70

 

(x+65+73)/3*0.7=53.5

 

x+65+73≈229

 

x≈91

 

 

Answer 2

let x be the third test grade

 

 

.7(65 + 73+ x) + .1(85) + .2(40) = .7

    210 + 10 + 20

 

.7(65 + 73+ x) + .1(85) + .2(40) = .7 (240)

 

.7(65 + 73+ x) + .1(85) + .2(40) = 168

 

45.5 + 51.1 + .7x + 8.5 + 8 = 168

 

.7x + 113.1 = 168

 

.7x = 54.9

 

x ≈ 78.43

 

Answer 3

Sales tax essentially adds on an amount to get to the final cost, so it would look like:

Price + Price * tax = final cost

It can also be written:

Price * 1.tax = final cost.

 

So we know the final price, and we know the tax:

1.08P =  $11.61

All we need to do now is isolate P by dividing both sides by 1.08:

P = $10.75

 

Now to find the tax, we take the final cost and subtract the original price.

$11.61 - $10.75 = .86

Answer 4

Brenda, this is a good question! If we let x be the original price, then we paid x + .08x for a total of 11.61.

 

x + .08x = 11.61

    1.08× = 11.61

            x = 10.75

 

11.61 - 10.75 = .94, so your answer is 94 cents. Hope this helps!