help solving 3 word problems!?? please?

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?

 

 

 

 

Sarah has 26 coins. Some are pennies and some are nickels. If the coins are worth 62 cents, how many are nickels?

 

 

 

 

In a certain course, there are two exams worth 30% each, a major paper worth 25% and quizzes worth 15%. If a student got scores of 84 on the first exam, and a 78 on the paper, and an average of 72 on the quizzes, what is the lowest score the student can get on the second test to have a semester average of 82?

Answer 1

For the second question concerning Sarah's coins,

Each nickle is 5 cents, and each penny is one cent.

Let N= number of nickles

Let (26-N)= number of pennies.

N(5cents)+(26-N)(1cents)=62cents

5Ncents+26cents-Ncent=62cents

4Ncents+26cents=62cents

4Ncents=36cents

N=9

 

Therefore, Sarah has 9 nickles and the rest are pennies(which means she has 17 pennies).