Question

A department store buyer ordered 430 shirts, some red, some white, and some blue. He ordered twice as many red as white and 50 more blue than white. How many of each color will there be?

a) 80 red, 30 white, 120 blue
b) 100 red, 50 white, 80 blue
c) 70 red, 35 white, 125 blue
d) 90 red, 45 white, 110 blue

Answer 1

To solve the algebra problem, we let w represent the number of white shirts, then calculated the red and blue shirts as 2w and w + 50 respectively. Solving w + 2w + (w + 50) = 430 revealed that there are 95 white, 190 red, and 145 blue shirts.

Step-by-step explanation:

The problem you've asked about is a classic algebra question where you need to determine the number of shirts of each color given the total number of shirts and the relationships between the numbers of each color. The department store buyer ordered a total of 430 shirts, and we are told there are twice as many red shirts as white, and 50 more blue shirts than white. Let's use w to represent the number of white shirts. Then the number of red shirts will be 2w (twice the number of white shirts), and the number of blue shirts will be w + 50 (50 more than the white shirts).

Now we can set up an equation to represent the total number of shirts:
w + 2w + (w + 50) = 430
Combining like terms gives us:
4w + 50 = 430
Subtracting 50 from both sides:
4w = 380
Dividing by 4:
w = 95

Now that we know there are 95 white shirts, we can calculate the other quantities:
2w = 2 × 95 = 190 (red shirts)
w + 50 = 95 + 50 = 145 (blue shirts)

Therefore, the correct answer is:
There will be 190 red shirts, 95 white shirts, and 145 blue shirts.