I Have A Couple Math Problems ..Can You Help?

Question

1. Lisa charges $25 for tutoring & $18 for a groupsession. One day in jan, Lisa earned $265 from 12 students. Howmany students of each type did lisa tutor?


2. A collection of quarters and nickles is worth $1.25. There are 13 coins in all. How many of each coin are there?



ThanX

Answer 1

1. 5 group sessions - 5 x 18 = 90
7 tutoring sessions - 7 x 25 = 175
90+175 = 265

You have to figure the 18 dollars out to an amount that would end with a 0 or 5 first.

2. 3 quarters = .75 cents
10 nickels = .50
.50 + .75 = 1.25
10+3 = 13

Answer 2

1. Let x = the number of people tutored, and y = the number in group sessions.

25x + 18y = 265
x + y = 12

Solving the second equation for y
y = 12 - x

Substituting that solution into the first equation
25x + 18(12-x) = 265
25x + 216 - 18x = 265
7x = 265 -216
7x = 4
x=7

Putting that into the second equation
y = 12-7
y = 5

7 people paid for tutoring sessions (for a total of $175) and 5 paid for a group session ($90).

2. Let q = the number of quarters and n = the number of nickels.
25q + 5n = 125
q + n = 13

Using similar steps as above
n = 13-q

25q + 5(13-q)=125
25q + 65 -5q = 125
20q = 60
q = 3

n = 13 - 3
n = 10

There are 3 quarters ($0.75) and 10 nickels ($0.50).

Answer 3

25(7) + 18(5) = 265

175 + 90 = 265

7 and 5.
I just plugged those in.

3 quarters and 10 nickles = 1.25

Answer 4

half of our problem - is knowing how to spell out the problem on paper

12 students and some paid $25 and the rest paid $18
x respresents the 25 crowd, so then 12-x is the rest
25X + 18(12-X) = 265

you can solve from here?

2) Q + N = 13
therefore Q = 13 - N (we subtracted N from both sides
second equation is
25q + 5n = 125
25(13-N) +5n = 125
and you have it from here


all the best

Answer 5

you need to set up a systems of equations for both questions.
for example, for # 1, use 25t + 18g = 265 and t + g = 12, and solve by using a method im guessing you learned in class (like substitution)