Jennifer had brochures printed for her new business venture. She originally ordered 5 boxes of black-and-white brochures and 3 boxes of color brochures, which cost a total of $125. After those ran out, she spent $145 on 5 boxes of black-and-white brochures and 4 boxes of color brochures. Given that the prices didn't change, what was the price of each type of brochure?
Let the price of each box of black-and-white brochures be x
The price of 5 boxes of black-and-white brochures is $5*x =$ <<5*x=5x>>5x
The price of 3 boxes of color brochures is $3*y =$ <<3*y=3y>>3y
The total cost of the brochures is 5x+3y= $125..........(1)
The price of 5 boxes of black-and-white brochures is $5*x =$ <<5*x=5x>>5x
The price of 4 boxes of color brochures is $4*y =$ <<4*y=4y>>4y
The total cost of the brochures is 5x+4y=$145..........(2)
Multiply equation (1) by 4 and equation (2) by 3, we have:
20x+12y=500............(3)
15x+12y = 435............(4)
By subtracting equation (4) from equation (3), we get:
20x-15x+12y-12y = 500-435
5x = 65
x = 65/5
x = $<<65/5=13>>13
Substituting the value of x in equation (1), we have:
5*13 + 3y = 125
65 + 3y = 125
3y = 125 - 65
3y = 60
y =60/3
y = $<<60/3=20>>20
Therefore the price of each box of black-and-white brochures is $13 and the price of each box of color brochures is $20. Answer: \boxed{13, 20}.
To keep in shape, Scott exercises at a track near his home. He requires 29 minutes to do 2 laps running and 5 laps walking. In contrast, he requires 30 minutes to do 10 laps running and 2 laps walking. Assuming he maintains a consistent pace while running and while walking, how long does Scott take to complete a lap?
Let's assume that the time it takes Scott to complete a lap running is "r" minutes, and the time it takes him to complete a lap walking is "w" minutes.
From the given information, we can create two equations:
2r + 5w = 29 (equation 1)
10r + 2w = 30 (equation 2)
We need to solve this system of equations to find the values of "r" and "w."
Multiplying equation 1 by 2 and equation 2 by 5, we get:
4r + 10w = 58 (equation 3)
50r + 10w = 150 (equation 4)
Subtracting equation 3 from equation 4, we get:
50r - 4r + 10w - 10w = 150 - 58
46r = 92
r = 92/46
r = 2
Now we can substitute the value of "r" into equation 1 to find "w."
2(2) + 5w = 29
4 + 5w = 29
5w = 29 - 4
5w = 25
w = 25/5
w = 5
Therefore, Scott takes 2 minutes to complete a lap running and 5 minutes to complete a lap walking.