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

Difference between revisions of "1963 TMTA High School Algebra I Contest Problem 38"

(Added problem and solution)
 
m (→‎Solution)
Line 15: Line 15:
  
  
−
The answer is <math>\boxed{(A)}</math>.
+
The answer is <math>\boxed{\text{(A)}}</math>.

Revision as of 11:37, 2 February 2021

Problem

A farmer sold $60$ hogs for $$2030.$ Some were sold for $$ 30$, and the remainder were sold for $$ 40$ each. How many were sold at $$ 30$ each?

$\text{(A)} \quad 37; \quad \text{(B)} \quad 19; \quad \text{(C)} \quad 29; \quad \text{(D)} \quad 42; \quad \text{(E)} \quad \text{none of these}$

Solution

If there were $h$ hogs sold at $30$ dollars each, then there were $60-h$ hogs sold at $40$ dollars each. Using this, we can construct an equation which lets us solve for $h$, the number of hogs sold at $30$ dollars each.

\[30h + 40(60-h) = 2030\] \[30h - 40h + 2400 = 2030\] \[-10h = -370\] \[h = \frac{-370}{-10} = 37.\]


The answer is $\boxed{\text{(A)}}$.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1963_TMTA_High_School_Algebra_I_Contest_Problem_38&oldid=144660"