|
Question 1109463: Mr. Johnson had some pears and apples in the ratio 5:2. He bought another 80 pears and the number of apples was one and a half times the number of pears. If 60 apples were sold, what was the new ratio of the number of apples to that of pears?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you did not specify whether the original ratio was pears to apples or apples to pears.
i originally assumed pears to apples = 5/2 and got a negative answer which is not possible.
i then assumed apples to pears = 5/2 and got a positive answer which is possible.
i therefore assumed that the original ratio of 5/2 had to be apples to pears, and not pears to apples.
if you let a = number of apples and p = number of pears, then the original ratio becomes:
a/p = 5/2
the problem states that, when he bought another 80 pears, that the number of apples became 1.5 times the number of pears.
the equation for that would be:
a = 1.5 * (p + 80)
from the ratio of a/p = 5/2, solve for p to get p = 2a/5.
in the equation of a = 1.5 * (p + 80), replace p with 2a/5 to get:
a = 1.5 * (2a/5 + 80)
simplify to get a = 1.5 * 2a/5 + 1.5 * 80
simplify further to get a = 3a/5 + 120
multiply both sides of this equation by 5 to get:
5a = 3a + 600
subtract 3a from both sides of the equation to get 2a = 600
solve for a to get a = 600 / 2 = 300
since p = 2a/5, replace a with 300 to get:
p = 2 * 300 / 5.
simplify to get p = 600 / 5
solve for p to get p = 600 / 5 = 120
you have solved for the original values of p and a.
they are a = 300 and p = 120.
the original ratio of a/p was 5/2.
a/p = 300 / 120 = 5/2
the original ratio is correct when a = 300 and p = 120.
when he added 80 pears, then he had 300 apples and 200 pears.
he then sold 60 apples, so he had 240 apples and 200 pears.
the ratio of apples to pears became 240 / 200 = 6/5.
the new ratio of apples to pears is 6/5.
that should be your solution.
|
|
|
| |
