1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lutik1710 [3]
3 years ago
14

You are fundraising for the schools track team by selling clothing. The first day, you sell 13 t-shirts and 17 pairs of shorts f

or a total of $385. The second day, you sell 13 t-shirts and 12 pairs of shorts for a total of $310.
How much does a t-shirt cost and how much does a pair of shorts cost?
Mathematics
1 answer:
Anastasy [175]3 years ago
6 0

Answers:

one t-shirt costs  $10

one pair of shorts costs  $15

============================================================

Explanation:

x = cost of one t-shirt

y = cost of one pair of shorts

13x+17y = 385 is the first equation because 13x represents the money you get from selling 13 shirts, and the 17y represents the amount you get from selling 17 shorts. The total 13x+17y is given to be $385

The second equation is 13x+12y = 310 for similar reasoning, but this time you sell 12 shorts this time and you get $310 in revenue.

The system of equations we have is:

\begin{cases}13x+17y = 385\\13x+12y=310\end{cases}

There are a few ways to solve this system. Possibly the quickest method is to note that the 13x shows up twice, so we can subtract straight down to eliminate the x terms

So,

  • 13x-13x becomes 0x or just 0, and the x terms go away.
  • 17y-12y becomes 5y
  • 385-310 becomes 75

After those three subtractions, we have the equation 5y = 75 which solves to y = 15 after dividing both sides by 5. This means the cost of one pair of shorts is $15

Plug this y value into any equation involving x and y, and solve for x

13x+17y = 385

13x+17(15) = 385

13x+255 = 385

13x = 385-255

13x = 130

x = 130/13

x = 10

Therefore, each t-shirt costs $10

-----------------

To help verify the answer, plug (x,y) = (10,15) into each equation. We should end up with a true result after simplifying both sides.

Start with the first equation

13x+17y = 385

13(10)+17(15) = 385

130+255 = 385

385 = 385

We get a true result which confirms the first equation.

Repeat for the second equation.

13x+12y = 310

13(10)+12(15) = 310

130+180 = 310

310 = 310

Both equations are true so (x,y) = (10, 15) has been fully confirmed.

You might be interested in
Jamie made 8 1 / 4 cups of fruit punch for a party.Her guests drank 2/3 of the punch .How much fruit punch did her guests?
Katen [24]
You can find a common demominator and then change 8 1/4 into a mixed number and just subtract
7 0
3 years ago
Triangles H J K and L M N are shown. The triangles have identical side lengths and angle measures. Triangle H J K is slightly lo
Hitman42 [59]

Answer:

The answer is b : translate K to N and reflect across the line containing JK

Step-by-step explanation:

I just took the quiz

4 0
3 years ago
15c² - 5c. Factorise completely ​
KATRIN_1 [288]

Looking at the problem, what we must do to complete this question is to completely factor the expression that was provided.  The expression that was provided is 15c^2 - 5c.

The first step that we must do is to take a look at the expression and see what the two pieces of the expression have in common.  We can see that both 15c^2 and -5c have the number 5 and the variable c associated with them so we can factor out those two.

<u>Factor out 5c</u>

  • 15c^2 - 5c
  • 5c(\frac{15c^2}{5c}) - 5c(\frac{5c}{5c})
  • 5c(3c) - 5c(1)
  • 5c(3c - 1)

Now we have completely factored out the expression that was provided in the problem statement and we came to final answer of 5c(3c - 1).

7 0
2 years ago
Read 2 more answers
Pls solve this...need help thanks :)​
WINSTONCH [101]

Step-by-step explanation:

2² * 3 * 5 = 4 * 3 * 5 = 60.

3² * 5² = 9 * 25 = 225.

7 0
3 years ago
Read 2 more answers
The perimeter it a square field is 224. How long is
geniusboy [140]
Since each side of a sqare is equal and there are four sides to the square
224 = 4x
X being the side length.
Then you would simiply divide by 4 to isolate x
x = 56
A side length is 56
8 0
3 years ago
Other questions:
  • As far as I know, the answer should be 100. That's not even a choice. Can anyone help me? If I can figure out how I'll give brai
    14·1 answer
  • Write a equation for the new circle obtained by translating the circle:
    14·1 answer
  • 2548 rounded to thousand
    9·2 answers
  • Solve the system using the substitution method:<br> 3x + 5y = -10<br> X - 5y =-10
    15·1 answer
  • Expand (5a/3 -2b/5)^3
    13·2 answers
  • There were 90 boys at the Hammarskjold school dance. They made up 60% of all of the students there. How many total students were
    6·1 answer
  • 5.4 Miles in 45 minutes
    11·1 answer
  • Sistemas de ecuaciones aplicando sustitucion me ayudan porfa
    14·1 answer
  • After cutting a piece 1.65 m long from a piece of cable, the remaining
    10·1 answer
  • Insert two rational number between 1.3 bar and 1.4 bar​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!