Question

Can you works at a bookstore he Packef 20 identical paper bags and 9 identical Textbook in a box the total mass of the box was 44.4 pounds after he put one more book and 5 more paperback in the Box the total mass of books was 51 lb write a system of equation that can be used to determine p and the mass and pound of one paperback and tea the mass in pounds of 1 textbooks.

then solve system of equation to find the tweo masses.

Answer 1

Let p be paper bags and t be textbooks. The system of equations would be

20p + 9t = 44.4
25p + 10t = 51

and the solution would be p = 0.75 and t = 3.27.

For the first equation, there were 20 paper bags and 9 textbooks for a total weight of 44.4 lbs. If p is the weight of the paper bags and t is the weight of the textbooks, we would multiply each by the number of items to find their weights.

For the second equation, there were 25 paper bags and 10 textbooks for a total weight of 51 pounds, by the same reasoning.

To solve this, we want the coefficients of one of the variables to be the same. We can do this by multiplying the first equation by 10 and the second equation by 9, to make the coefficients of t the same:

10(20p + 9t = 44.4) → 200p + 90t = 444
9(25p + 10t = 51) → 225p + 90t = 459

Subtracting the equations, we have:
200p + 90t = 444
-(225p + 90t = 459)

-25p = -15

Divide both sides by -25:
p = -15/-25 = 0.75

Plug this back into the first equation:
20(0.75) + 9t = 44.4
15 + 9t = 44.4

Subtract 15 from both sides:
9t = 29.4

Divide both sides by 9:
t = 3.27