Difference between revisions of "1956 AHSME Problems/Problem 4"

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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
 
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>
 
<cmath>2500 \cdot \frac{x}{1000} = 160.</cmath>
Solving, we get <math>x = \boxed{\textbf{(E)} \quad 6.4\%.}</math>
+
Solving, we get <math>x = \boxed{\textbf{(E) }6.4\%.}</math>
 
 
  
 
==See Also==
 
==See Also==

Latest revision as of 17:11, 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 (ProblemsAnswer KeyResources)
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

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