Question

If p represents number of boys and q represents number of girls, the coefficients of p and q represents the number of rows. Explain $2p + 4q = 44$ , $3p + 2q = 46$ in sentence form.

Answer 1

Hint: We can use the terms boys and girls in the place of the variables. Then we can take the given meaning of the coefficients. Then can apply the operations given in the equations and formulate the required sentence.

Complete step-by-step answer:
It is given that p is the number of boys.
It is also given that q represents the number of girls.
As the coefficients of p and q are the number of rows, we can take p and q as the number of boys and girls in each row respectively.
We can write the 1st equation as $2p + 4q = 44$ .
It can be stated as 2 times p added to 4 times q gives 44.
From the definitions of variables and coefficients, we can say that the sum of the number of boys in 2 rows and number of girls in 4 rows is 44.
Now we can take the 2nd equation $3p + 2q = 46$
It can be stated as 3 times p added to 2 times q gives 46.
From the definitions of variables and coefficients, we can say that the sum of the number of boys in 3 rows and number of girls in 2 rows is 46.
Therefore, the required statements are:
The sum of the number of boys in 2 rows and number of girls in 4 rows is 44 and the sum of the number of boys in 3 rows and number of girls in 2 rows is 46.

Note: Even though it is given that the variables p and q are the number of boys and girls, we must take them as the number of boys and girls in one row. We must not take the variables as the total number of boys and girls. We must take the variables as the number of rows and not as the nth row where n is the coefficient. We can solve the 2 equations to find the number of boys and girls.