Question

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 30 books. A total of 9 boxes were sent which can hold 240 books altogether. Graphically solve a system of equations in order to determine the number of small boxes sent, x,x, and the number of large boxes sent, yy.

Answer 1

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Answer 2

Solution :- Let us assume that, the number of small boxes sent are x and the number of large boxes sent are y.

so,

→ x + y = 9 ----------- Eqn.(1)

and,

→ Total books in small boxes = 20 * x = 20x books.

→ Total books in large boxes = 30 * y = 30y books.

then,

→ Total books in both boxes = 240

→ 20x + 30y = 240

→ 10(2x + 3y) = 240

→ 2x + 3y = 24 ------------ Eqn.(2)

Multiply Eqn.(1) by 2 and subtract from Eqn.(2),

→ (2x + 3y) - 2(x + y) = 24 - 2 * 9

→ 2x - 2x + 3y - 2y = 24 - 18

→ y = 6 boxes .

putting value of y in Eqn.(1),

→ x + 6 = 9

→ x = 9 - 6

→ x = 3 boxes .

Hence, Number of small boxes are 3 and Number of large boxes are 6.