Question

Max has a drawer full of green and red socks. He has three times as many red socks subtracted from four times as many green socks, which he believes is 50 socks. Half the number of green socks plus one-third of the number of red socks is 36. How many of each color does he have?

a) 14 green socks and 8 red socks
b) 12 green socks and 6 red socks
c) 16 green socks and 10 red socks
d) 18 green socks and 12 red socks

Answer 1

Max has 44 green socks and 42 red socks, which can be determined by setting up a system of equations based on the given information and solving for the two variables.

Step-by-step explanation:

To solve for the number of green and red socks Max has, we can set up two equations based on the information given:

1. Four times the number of green socks minus three times the number of red socks equals 50: 4G - 3R = 50.
2. Half the number of green socks plus one-third the number of red socks equals 36: 1/2 G + 1/3 R = 36.

Let G represent the number of green socks and R represent the number of red socks. To solve the equations simultaneously, we can multiply the second equation by 6 to eliminate the fractions:
3G + 2R = 216. Next, we can use the substitution or elimination method to solve for G and R.

By using elimination, we can multiply the first equation by 2 and the second by 3 to make the coefficients of R the same:

• 8G - 6R = 100
• 9G + 6R = 648

Adding these equations together, we get 17G = 748, which simplifies to G = 44. Now we can substitute this value of G into one of the original equations to find R:

1. 4(44) - 3R = 50
2. 176 - 3R = 50
3. 3R = 126
4. R = 42

Therefore, Max has 44 green socks and 42 red socks.