A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $400 and the daily rate for each partner is $1300. The law firm assigned 2 more associates than partners to the case and was able to charge the client $4200 per day for these lawyers' services. Determine the number of associates assigned to the case and the number of partners assigned to the case. Charlotte runs a farm stand that sells bananas and raspberries. Each pound of bananas sells for $3.25 and each pound of raspberries sells for $1.75. Charlotte sold 13 more pounds of bananas than pounds of raspberries and made $227.25 altogether. Determine the number of pounds of bananas sold and the number of pounds of raspberries sold.

1. The number of associates =  4

The number of partners = 2

2. Pounds of bananas sold = 50

Pounds of raspberries sold = 37

Step-by-step explanation:

1. Let,

Number of associates = x

Number of partners = y

According to given statement;

x = y + 2      Eqn 1

400x + 1300y = 4200     Eqn 2

Putting value of x from Eqn 1 in Eqn 2

400(y+2)+1300y=4200

400y+800+1300y=4200

1700y=4200-800

1700y = 3400

Dividing both sides by 1700

Putting y = 2 in Eqn 1

x = 2 + 2

x = 4

Hence,

The number of associates =  4

The number of partners = 2

2. Let,

b represents the pounds of bananas

r represent the pounds of raspberries

According to given statement,

b = r + 13     Eqn 1

3.25b + 1.75r = 227.25     Eqn 2

Putting value of b from Eqn 1 in Eqn 2

3.25(r+13) + 1.75r = 227.25

3.25r + 42.25 + 1.75r = 227.25

5r = 227.25-42.25

5r = 185

Dividing both sides by 5

Putting r = 37 in Eqn 1

b = 37+13 = 50

Hence,

Pounds of bananas sold = 50

Pounds of raspberries sold = 37

x/3-10=8

x/3=18

x=48