Karin's mom runs a dairy farm. Last year Betty the cow gave 375 litres less than twice the amount the amount from Bessie the cow. Together Betty and Bessie produced 1464 litres of milk . How many litres did each cow produced.

The volume of milk each cow produce are:

Betty = 851 litres

Bessie = 613 litres

Step-by-step explanation:

Let the volumes of milk from each of them be:

Betty = X litres

Bessie = Y litres

We are given the following information:

X = 2Y - 375 . . . . . . (1)     (Betty the cow gave 375 litres less than twice the amount the amount from Bessie the cow)

X + Y = 1464 . . . . . . (2)    (Together Betty and Bessie produced 1464 litres of milk)

Next, we will replace the value of 'X' in equation (2) with equation (1) as follows:

X = 2Y - 375 . . . . . . (1)  ;   X + Y = 1464 . . . . . . (2)

Therefore, equation (2) becomes:

(2Y - 375) + Y = 1464

2Y + Y - 375 = 1464

3Y - 375 = 1464

3Y = 1464 + 375 = 1,839 (divide both sides by 3)

∴ Y = 1839 ÷ 3 = 613 litres

Finally, from equation 2, we have X + Y = 1464 ; since Y = 613, solving for X:

X + Y = 1464

X + 613 = 1464

X = 1464 - 613 = 851 litres

Therefore:

Betty (X) = 851 litres

Bessie (Y) = 613 litres