He spent a total of $112 on 14 music purchases. one Music CDs were on sale for $10 and cassettes were on sale for $3. How much did Andrew pay for each music CD and each cassette tape?

Question
Equations and inequalities
asked 2021-03-07
He spent a total of $112 on 14 music purchases. one Music CDs were on sale for $10 and cassettes were on sale for $3. How much did Andrew pay for each music CD and each cassette tape?

Answers (1)

2021-03-08
M = Music CDs
C = cassettes
Create two equations, one for the number of music purchases he made (14) and one for the price of the music purchases ($112)
M + C = 14 ( this is the number of music purchases he made)
10M + 3C = 112 ( this is the price of the music purchases)
Isolate a variable, I isolated M
M + C = 14
M = 14 - C
Subsitute that variable into the other equation
10 M + 3C = 112
10(14-C) + 3C = 112 ( substitute our previous equation into M)
140 - 10C + 3C = 112
-10C + 3C = -28
-7C = -28
C = 4
Plug C back into either equation, I chose the simpler one
M + C = 14
M + (4) = 14
M = 10
Since he bought 4 cassettes for $3 dollars each 4($3) = $12 worth of cassettes.
Since he bought 10 Music CDs for $10 dollars each 10($10) = $100 worth of cassettes.
0

Relevant Questions

asked 2020-11-29
Lynne bought a bag of grapefruit, \(1\frac{5}{8}\) pounds of apples, and \(2\frac{3}{16}\) pounds of bananas. The total weight of her purchases was \(7\frac{1}{2}\) pounds. How much did the bag of grapefruit weigh?
asked 2020-10-23
Chuck receives loans totaling $12,000 from two ba
. One bank charges 7.5% annual interest, and the second bank charges 6% annual interest. He paid $840 in total interest in one year. How much was loaned at each bank?
asked 2021-02-25
Celine, Devon, and another friend want to purchase some snacks that cost a total of $7.50. They will share the cost of the snacks. Which of these statements is true?
A. An equation that can be used to find x, the amount of money each person will pay is x+3=7.5. The solution to the equation is 4.5, so each person will pay $4.50.
B. An equation that can be used to find x, the amount of money each person will pay is x+3=7.5. The solution to the equation is 10.5, so each person will pay $10.50.
C. An equation that can be used to find x, the amount of money each person will pay is x⋅3=7.5. The solution to the equation is 2.5, so each person will pay $2.50.
D. B. An equation that can be used to find x, the amount of money each person will pay is x⋅3=7.5. The solution to the equation is 22.5, so each person will pay $22.50.
asked 2020-11-09
A store sells small notebooks for $8 and large notebooks for $10. If you buy 6 notebooks and spend $56, how many of each size notebook did you buy?
asked 2021-02-12
Luke has a credit limit of $8,500 on his credit card. He had a previous balance of $4,236.87 and made a $3,200.00 payment. The total of his purchases is $989.42. What is Luke's available credit?
asked 2021-02-27
Vince worked 18 hours last week. Part of the time he worked in a fast-food restaurant and part of the time he worked tutoring a high school student in mathematics. He was paid $7.25 per hour working in the restaurant and $15 per hour tutoring. If he earned $161.50, how many hours did he work at each job?
asked 2021-02-24
A 1966 Andy Warhol portrait of Marlon Brando on his motorcycle sold for $5 million at Christie's in 2003. On November 14, 2012, the work was sold again by Christie's for about 4 4/5 times the amount paid in 2003. How much was paid for the portrait in 2012?
asked 2020-10-20
Last Saturday, 1,750 people attended an event at Farway Gardens. The admission fee was $3.50 for children and $8.00 for adults. If the total amount of money collected at the event was $9,860, how many children and how many adults attended the event?
asked 2021-02-06
You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save $75 per week, and your friend saves $50 per week. When the vacation time comes, you have $950, and your friend has $800. How much did you start with, and for how many weeks did you save?
A. $150, 8 weeks
B. $75, 3 weeks
C. $500, 5 weeks
D. $500, 6 weeks
asked 2021-02-08
At a recent production of A Comedy of Errors, the Community Theater brought in a total of $30,495 in revenue. If adult tickets were $9 and children's tickets were $6.50, how many tickets of each type were sold if 3800 tickets in all were sold?
...