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 "1956 AHSME Problems/Problem 4"

(Created page with "==Problem #4== ==Solution== ==See Also== {{AHSME 50p box|year=1956|num-b=3|num-a=5}} Category:Introductory Algebra Problems {{MAA Notice}}")
 
(→‎Solution)
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
 
==Problem #4==
 
==Problem #4==
 +
 +
A man has <math>\textdollar{10,000 }</math> to invest. He invests <math>\textdollar{4000}</math> at 5% and <math>\textdollar{3500}</math> at 4%.
 +
In order to have a yearly income of <math>\textdollar{500}</math>, he must invest the remainder at:
  
 +
<math>\textbf{(A)}\ 6\%\qquad\textbf{(B)}\ 6.1\%\qquad\textbf{(C)}\ 6.2\%\qquad\textbf{(D)}\ 6.3\%\qquad\textbf{(E)}\ 6.4\% </math>
 
==Solution==
 
==Solution==
 +
The man currently earns <math>4000 \cdot \frac{5}{1000} + 3500 \cdot \frac{4}{1000} = 340</math> dollars. So, we need to find the value of <math>x</math> such that
 +
<cmath>2500 \cdot \frac{x}{1000} = 160.</cmath>
 +
Solving, we get <math>x = \boxed{\textbf{(E) }6.4\%.}</math>
  
 
==See Also==
 
==See Also==

Latest revision as of 16:11, 14 March 2023

Problem #4

A man has $\textdollar{10,000 }$ to invest. He invests $\textdollar{4000}$ at 5% and $\textdollar{3500}$ at 4%. In order to have a yearly income of $\textdollar{500}$, he must invest the remainder at:

$\textbf{(A)}\ 6\%\qquad\textbf{(B)}\ 6.1\%\qquad\textbf{(C)}\ 6.2\%\qquad\textbf{(D)}\ 6.3\%\qquad\textbf{(E)}\ 6.4\%$

Solution

The man currently earns $4000 \cdot \frac{5}{1000} + 3500 \cdot \frac{4}{1000} = 340$ dollars. So, we need to find the value of $x$ such that \[2500 \cdot \frac{x}{1000} = 160.\] Solving, we get $x = \boxed{\textbf{(E) }6.4\%.}$

See Also

1956 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 3 		Followed by
Problem 5
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1956_AHSME_Problems/Problem_4&oldid=190964"