Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1963 TMTA High School Algebra I Contest Problem 18

Revision as of 10:24, 2 February 2021 by Coolmath34 (talk | contribs) (Created page with "== Problem == A dealer packed <math>1800</math> basketballs in <math>6</math> barrels and <math>6</math> boxes. Later he packed <math>2250</math> basketballs in <math>9</math>...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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.

See Also

1963 TMTA High School Mathematics Contests (Problems)
Preceded by
Problem 17 		TMTA High School Mathematics Contest Past Problems/Solutions Followed by
Problem 19
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1963_TMTA_High_School_Algebra_I_Contest_Problem_18&oldid=144617"