oranges --- x
apples ---- x + 32
overripe oranges = (3/5)x
overripe apples = (1/3)(x+32)
but they are the same ....
(1/3)(x+32) = (3/5)x
multiply by 15 , the LCD
5(x+32) = 9x
5x + 160 = 9x
160 = 4x
x = 40
overripe fruit = (1/3)(x+32) + (3/5)x
= (1/3)(72) + (3/5)(40) = 48
check
oranges = 40
apples = 72
overripe oranges = (3/5)(40) = 24
overripe apples = (1/3)(72) = 24
total overripe = 24+24 = 48
There are 32 more apples than oranges in a box. 3/5 of the oranges and 1/3 of the apples are overripe. If the number of overripe apples and the number of overripe oranges are the same, how many pieces of overripe fruit are there?
2 answers
It’s much easier to draw 2 bars. The first is for apples and you split it into 3 equal lengths. Underneath you draw the bar for oranges which you split into 5 equal lengths, making sure that 3/5 is the same length as the 1/3 above it. Split your thirds into thirds to make ninths and now you know that 4/9 of the apples is 32 so 1/9 is 8 apples. There are 8 oranges in each 1/5 so if 3/5 are over ripe, this is 24 oranges. 1/3 of the apples are over ripe - also 24. 24+24 =48 over ripe pieces of fruit!!
1 answer