1963 TMTA High School Algebra I Contest Problem 18

Problem

A dealer packed $1800$ basketballs in $6$ barrels and $6$ boxes. Later he packed $2250$ basketballs in $9$ barrels and $7$ boxes. Find the number of basketballs that a barrel will hold.

$\text{(A)} \quad 75 \quad \text{(B)} \quad 225 \quad \text{(C)} \quad 150 \quad \text{(D)} \quad 25 \quad \text{(E) NOTA}$

Solution

Suppose a barrel can hold $x$ basketballs and a box can hold $y$ basketballs. We can write the following system of equations: $6x+6y = 1800$ $9x+7y = 2250$ Solving, we find that $(x, y)=(75, 225),$ so a barrel can hold $\boxed{\text{(A)} \quad 75}$ basketballs.

1963 TMTA High School Mathematics Contests (Problems)
Preceded by Problem 17	TMTA High School Mathematics Contest Past Problems/Solutions	Followed by Problem 19

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1963 TMTA High School Algebra I Contest Problem 18

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