Word Fraction

Question

at Aaron's fruit stand, 3/4 of the apples were red and the rest were green. He sold 1/2 of the total number of apples. 5/6 of the apples sold were red. 28 green apples were left. How many red apples did Aaron sell?

Answer 1

X is the total number of apples

(3/4)X are red and (1/4)X are green

half of the apples sold ---> X/2 were sold

5/6 of the apples sold were red, so (5/6)(1/2)x = (5/12)x were red...

(1/2)x - (5/12)x = (6/12)x - (5/12)x = (1/12)x were green apples sold

total # of green apples = # of green apples sold + # of green apples NOT sold

(1/4) X = (1/12)x + 28

multiplies the equation by 12

3x = x + 336

2x = 336

x = 336/2 = 168

168 apples...... (3/4)*168 = 126 red and 168-126 - 42 green. Note than 42/168 = 1/4

Half of the apples are sold, so 84 sold.

5/6 * 84 = 5*84/6 = 5*14 = 70 of those sold were red.

so then 14 of them were green.... 14/84 = 1/6..

70 red apples sold