Question

On a recent trip to a local orchard, the Morgan family picked four different kinds of apples - Braeburn, Cortland, Fuji, and Rome. When they were done, they discovered that they had picked

a. a total of 360 apples,
b. twice as many Braeburn as Fuji,
c. twice as many Cortland as Rome,
d. 50% more Fuji than Rome.

How many of each kind of apple did they pick?

Answer 1

Morgan family picked 144 Braeburn apples, 96 Cortland apples, 72 Fuji apples and 48 Rome apples.

Explanation:

Let B, C, F and R represent Braeburn apples, Cortland apples, Fuji apples, and Rome apples respectively.

We have been given that Morgan family picked a total of 360 apples. We can represent this information in an equation as:

`B+C+F+R=360...(1)`

We are told that Morgan family picked twice as many Braeburn as Fuji. We can represent this information in an equation as:

`B=2F...(2)`

We are told that Morgan family picked twice as many Cortland as Rome, that is:

`C=2R...(3)`

We are told that Morgan family picked 50% more Fuji than Rome, that is:

`F=1.5R...(4)`

Upon substituting equation (4) in equation (2), we will get:

`B=2(1.5)R`

`B=3R`

Now, each apple in in terms of Rome apples, so we will get:

`3R+2R+1.5R+R=360`

Let us solve for R.

`7.5R=360`

`(7.5R)/(7.5)=(360)/(7.5)`

`R=48`

Therefore, Morgan family picked 48 Rome apples.

Upon substituting
`R=48` in (3), we will get:

`C=2R\Rightarrow 2(48)=96`

Therefore, Morgan family picked 96 Cortland apples.

Upon substituting
`R=48` in (4), we will get:

`F=1.5R\Rightarrow 1.5(48)=72`

Therefore, Morgan family picked 72 Fuji apples.

Upon substituting
`F=72` in (2), we will get:

`B=2F\Rightarrow 2(72)=144`

Therefore, Morgan family picked 144 Braeburn apples.