Respuesta :
Answer:
Morgan family picked 144 Braeburn apples, 96 Cortland apples, 72 Fuji apples and 48 Rome apples.
Step-by-step 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:
[tex]B+C+F+R=360...(1)[/tex]
We are told that Morgan family picked twice as many Braeburn as Fuji. We can represent this information in an equation as:
[tex]B=2F...(2)[/tex]
We are told that Morgan family picked twice as many Cortland as Rome, that is:
[tex]C=2R...(3)[/tex]
We are told that Morgan family picked 50% more Fuji than Rome, that is:
[tex]F=1.5R...(4)[/tex]
Upon substituting equation (4) in equation (2), we will get:
[tex]B=2(1.5)R[/tex]
[tex]B=3R[/tex]
Now, each apple in in terms of Rome apples, so we will get:
[tex]3R+2R+1.5R+R=360[/tex]
Let us solve for R.
[tex]7.5R=360[/tex]
[tex]\frac{7.5R}{7.5}=\frac{360}{7.5}[/tex]
[tex]R=48[/tex]
Therefore, Morgan family picked 48 Rome apples.
Upon substituting [tex]R=48[/tex] in (3), we will get:
[tex]C=2R\Rightarrow 2(48)=96[/tex]
Therefore, Morgan family picked 96 Cortland apples.
Upon substituting [tex]R=48[/tex] in (4), we will get:
[tex]F=1.5R\Rightarrow 1.5(48)=72[/tex]
Therefore, Morgan family picked 72 Fuji apples.
Upon substituting [tex]F=72[/tex] in (2), we will get:
[tex]B=2F\Rightarrow 2(72)=144[/tex]
Therefore, Morgan family picked 144 Braeburn apples.
