Question

I have a mixture of 135 M&Ms. They come in the colors, red, blue, yellow and brown. There are five more blue M&Ms than red ones. The number of yellow M&Ms is nine less than the number of red ones. The number of brown M&Ms is thirteen more than half the number of red ones. Find the number of red, blue, yellow and brown M&Ms.

Answer 1

Explanation:

r: the number of red M&Ms

b: the number of blue M&Ms

y: the number of yellow M&Ms

br: the number of brown M&Ms

We can translate the given information into equations:

r + b + y + br = 135 (the total number of M&Ms is 135)

b = r + 5 (there are five more blue M&Ms than red ones)

y = r - 9 (there are nine less yellow M&Ms than red ones)

br = 13 + (1/2)r (there are thirteen more brown M&Ms than half the number of red ones)

We can use equations 2, 3, and 4 to substitute for b, y, and br in equation 1:

r + (r + 5) + (r - 9) + (13 + (1/2)r) = 135

Simplifying this equation, we get:

3.5r + 9 = 135

Subtracting 9 from both sides, we get:

3.5r = 126

Dividing both sides by 3.5, we get:

r = 36

Now that we know the value of r, we can use equations 2, 3, and 4 to find the values of b, y, and br:

b = r + 5 = 36 + 5 = 41

y = r - 9 = 36 - 9 = 27

br = 13 + (1/2)r = 13 + (1/2)(36) = 31

Therefore, the number of red, blue, yellow, and brown M&Ms in the mixture are 36, 41, 27, and 31, respectively.

Answer 2

Let x be the number of red M&Ms.

Then the number of blue M&Ms is x + 5, the number of yellow M&Ms is x - 9, and the number of brown M&Ms is (1/2)x + 13.

The total number of M&Ms is 135, so we can write an equation:

x + (x + 5) + (x - 9) + (1/2)x + 13 = 135

Simplifying this equation, we get:

3.5x + 9 = 135

Subtracting 9 from both sides, we get:

3.5x = 126

Dividing both sides by 3.5, we get:

x = 36

So there are 36 red M&Ms, 41 blue M&Ms (36 + 5), 27 yellow M&Ms (36 - 9), and 31 brown M&Ms (1/2 * 36 + 13).