Josh and Racquel sold corn dogs and burritos at the math club fundraiser. The corn dogs(c) cost $.35, and the burritos(b) cost $.75. They sold a total of 600 items, and raised $360.
a)Write an equation for the total # of items sold.
b)Write and equation for the total cost of the items.
c) The equations form a system. Solve the system to find the # of corn dogs and burritos sold.
~my answers~
a) c+b=600
b)$.35c+$.75b=$360
c) c=225
b=375
Firstly, I find it weird to sell corn dogs and burritos together. Still, I would love to know if I got it right.
Oh and what is a matrix? I have to make one for the system, but i can't even remember what they are! (how the heckz did i pass my finals?!?)
Anyway, any help would be very much appreciated. Thanks!
Your answers are correct.
A matrix is a set of rows and columns of numbers. In this case the numbers of the matrix would be the coefficients of c and b in the two equations, or the coefficients of one variable and the sum. They can be used to solve systems of linear equations such as these. For example
c =
|600 1|
|360 .75|
__________
|1 1|
|.35 .75|
= (450-360)/(.75-.35) = 90/.4 = 225
Thank you so much!
c=
600 1
360.75
1 1
.35.75
= 450-360
.75-.35=90
.4=225
You did a great job with your answers! Let's go through them to confirm:
a) The equation for the total number of items sold is correct: c + b = 600. This equation represents the fact that the number of corn dogs sold (c) added to the number of burritos sold (b) equals the total number of items sold (600).
b) The equation for the total cost of the items is also correct: 0.35c + 0.75b = 360. In this equation, we multiply the cost of each corn dog ($0.35) by the number of corn dogs sold (c), add it to the result of multiplying the cost of each burrito ($0.75) by the number of burritos sold (b), and set the whole expression equal to the total amount raised ($360).
Now, let's solve the system of equations to find the number of corn dogs and burritos sold:
To solve the system, we can use a method called substitution. Let's start by solving equation a) for c: c = 600 - b.
Now, we can substitute c in equation b) with 600 - b:
0.35(600 - b) + 0.75b = 360.
Next, let's distribute and simplify:
210 - 0.35b + 0.75b = 360.
Combine like terms:
0.40b = 150.
Divide both sides by 0.40:
b = 150 / 0.40.
Calculating this, we get b = 375.
Now, substitute the value of b back into the equation c = 600 - b:
c = 600 - 375.
Calculating, we find that c = 225.
So the final solution is c = 225 and b = 375, just as you have correctly determined.
Great job on solving the system!
Regarding your question about matrices, a matrix is a rectangular array of numbers or variables arranged in rows and columns. In this context, we don't need to use matrices to solve this system of equations. However, matrices are often used in more advanced mathematics and can be useful for solving larger systems of equations or performing other mathematical operations.