SOLUTION: I need to write an equation to show what X and Y are and solve for X and Y Question 1- "A 110 point final exam is mad up of 50 questions. Some questions are worth 2 points and s

Algebra ->  Linear-equations -> SOLUTION: I need to write an equation to show what X and Y are and solve for X and Y Question 1- "A 110 point final exam is mad up of 50 questions. Some questions are worth 2 points and s      Log On


   

Question 1017276: I need to write an equation to show what X and Y are and solve for X and Y
Question 1- "A 110 point final exam is mad up of 50 questions. Some questions are worth 2 points and some are worth 4 points. How many of each type of question are on the test?"
Question 2- "One gym charges $40 per month and $3 per exercise class. Another gym charges $20 per month and $8 per exercise class. After how many exercise classes will the monthly cost be the same and what will that cost be?"
Question 3- "Martha went to the movies. She purchased some $14 movie tickets and some 412 movie tickets. She purchased a total of $9 tickets for $114. How many of each type of ticket did she buy?"
Question 4(final)- "A small soda costs $0.45 and a large soda costs $0.65. 35 sodas were sold for a total of $18.55. How many of each size soda were sold?"
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Question 1- "A 110 point final exam is made up of 50 questions. Some questions are worth 2 points and some are worth 4 points. How many of each type of question are on the test?"
.
T=number of 2 point questions; F=number of 4 point questions
.
T+F=50
T=50-F . Use this to substitute for T below.
.
2T+4F=110 . Substitute for T from above.
2(50-F)+4F=110
100-2F+4F=110
2F=10
F=5
.
ANSWER 1: There were 5 four point questions.
.
T=50-F=50-5=45
.
ANSWER 2: There were 45 two point questions.
.
CHECK:
2T+4F=110
2(45)+4(5)=110
90+20=110
110=110
.
Question 2- "One gym charges $40 per month and $3 per exercise class. Another gym charges $20 per month and $8 per exercise class. After how many exercise classes will the monthly cost be the same and what will that cost be?"
.
x=number of classes
.
$40+$3x=$20+$8x
$20+$3x=$8x
$20=$5x
4=x
.
ANSWER 1: The cost will be the same for 4 classes.
.
$40+$3(4)=$40+$12=$52
ANSWER 2: The monthly cost for four classes from either gym is $52.
.
CHECK:
$40+$3x=$20+$8x
$40+$3(4)=$20+$8(4)
$40+$12=$20+$32
$52=$52
.
Question 3- "Martha went to the movies. She purchased some $14 movie tickets and some $12 movie tickets. She purchased a total of 9 tickets for $114. How many of each type of ticket did she buy?"
.
T=$12 tickets; F=$14 tickets
.
T+F=9
F=9-T
.
$12T+$14F=$114
$12T+$14(9-T)=$114
$12T-$$126-$14T=$114
-$2T=-$12
T=6
.
F=9-T=9-6=3
.
ANSWER:She bought six $12 tickets and three $14 tickets.
.
CHECK:
$12T+$14F=$114
$12(6)+$14(3)=$114
$72+$42=$114
$114=$114
.
Question 4(final)- "A small soda costs $0.45 and a large soda costs $0.65. 35 sodas were sold for a total of $18.55. How many of each size soda were sold?"
.
S=small sodas; L=large sodas
.
S+L=35
S=35-L
.
$0.45S+$0.65L=$18.55
$0.45(35-L)+$0.65L=$18.55
$15.75-$0.45L+$0.65L=$18.55
$0.20L=$2.80
L=14
.
S=35-L=35-14=21
ANSWER: 14 large and 21 small sodas were sold.
.
CHECK:
$0.45S+$0.65L=$18.55
$0.45(21)+$0.65(14)=$18.55
$9.45+$9.10=$18.55
$18.55=$18.55
.
IN THE FUTURE, PLEASE LIMIT TO ONE QUESTION PER POST.