A chef ordered a total of 250 potatoes and carrots. He ordered 20 fewer potatoes than carrots. He then used 3 times as many potatoes as carrots. The number of potatoes left was half the number of carrots left.
(a) How many carrots did he order?
(b) How many potatoes were left?
(a) Let us say potatoes are equal to x
carrots are equal to y.
Then the question we know
x + y = 250 - (i)
x + 20 = y - (ii)
(ii) equation
x = y - 20 put this in eq (i)
y - 20 + y = 250
2y = 250 + 20
2y = 270
y = 135
put this in eq (i)
x + 135 = 250
x = 250 - 135
x = 115
x = 115, y = 135
So he ordered 135 carrots
(b) Let us say the chef used 3 carrots
We can get
= 115 - 3y = 1/2 (135 - y)
= 115 - 3y = 1/2 * 135 - 1/2y
= 115 - 3y = 67.5 - 1/2y
= 115 - 67.5 = -1/2y + 3y/1
= 47.5 = (-1 + 6)/2 y
= 47.5 = 8/2y
= 47.5 = 2.5y
= 47.5/2.5 = y
= 19 = y
y = 19
so
115 - 3 * 19 + 115 - 57 = 58
So 58 potatoes were left
