Examkin

Question

Difficulty: MediumRatios, Rates, and Proportions

A commercial printing facility uses three high-speed printers—Printer X, Printer Y, and Printer Z—to produce advertising brochures. The ratio of the number of brochures printed by Printer X to Printer Y during a morning shift is 3:53:5. During the same shift, the ratio of the number of brochures printed by Printer Y to Printer Z is 4:34:3. If Printer Z printed 1,8001,800 brochures during the shift, what is the total number of brochures printed by all three printers combined?

  1. A
    3,8403,840
  2. B
    3,9603,960
  3. 5,6405,640Answer
  4. D
    6,6006,600
  5. E
    7,0507,050

Answer

The total number of brochures printed by all three printers combined is 5,6405,640.
To find the total printed brochures, determine the output of each printer step by step. Using the ratio of Printer Y to Printer Z (4:34:3), since Printer Z printed 1,8001,800 brochures, Printer Y printed 43×1,800=2,400\frac{4}{3} \times 1,800 = 2,400 brochures. Using the ratio of Printer X to Printer Y (3:53:5), Printer X printed 35×2,400=1,440\frac{3}{5} \times 2,400 = 1,440 brochures. Adding the amounts for all three printers gives 1,440+2,400+1,800=5,6401,440 + 2,400 + 1,800 = 5,640 brochures.

Step-by-Step Solution

1
Calculate the output of Printer Y using the ratio of Printer Y to Printer Z.
Printer Y printed 43×1,800=2,400\frac{4}{3} \times 1,800 = 2,400 brochures.
The ratio of Printer Y to Printer Z is 4:34:3, so Printer Y produced 43\frac{4}{3} times as many brochures as Printer Z.
2
Calculate the output of Printer X using the ratio of Printer X to Printer Y.
Printer X printed 35×2,400=1,440\frac{3}{5} \times 2,400 = 1,440 brochures.
The ratio of Printer X to Printer Y is 3:53:5, so Printer X produced 35\frac{3}{5} times as many brochures as Printer Y.
3
Sum the outputs of all three printers.
1,440+2,400+1,800=5,6401,440 + 2,400 + 1,800 = 5,640 brochures.
The question asks for the total combined production of Printer X, Printer Y, and Printer Z.

Key Concept

Combining rates or proportions involving shared quantities by setting up equivalent proportional relationships.
Estimated Time:1m 30s
Rate this question

Topics

Ratios, Rates, and Proportions

More questions from this topic