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Difference between revisions of "1957 AHSME Problems/Problem 8"

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==Solution==
 
==Solution==
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In order to solve the problem, we first need to find each of the three variables. We can use the proportions the problem gives us to find the value of one part, and, by extension, the values of the variables (as <math>x</math> would have <math>2</math> parts, <math>y</math> would have <math>3</math>, and <math>z</math> would have <math>5</math>). One part, after some algebra, equals <math>10</math>, so <math>x</math>, <math>y</math>, and <math>z</math> are <math>20</math>, <math>30</math>, and <math>50</math>, respectively.
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We can plug <math>x</math> and <math>y</math> into the equation given to us: <math>30 = 20a-10</math>, and then solve to get <math>a = \boxed{\textbf{(A)}2}</math>.
 
==See Also==
 
==See Also==
 
{{AHSME box|year=1957|num-b=7|num-a=9}}
 
{{AHSME box|year=1957|num-b=7|num-a=9}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 15:40, 12 October 2020

The numbers $x,\,y,\,z$ are proportional to $2,\,3,\,5$. The sum of $x, y$, and $z$ is $100$. The number y is given by the equation $y = ax - 10$. Then a is:

$\textbf{(A)}\ 2 \qquad \textbf{(B)}\ \frac{3}{2}\qquad \textbf{(C)}\ 3\qquad \textbf{(D)}\ \frac{5}{2}\qquad \textbf{(E)}\ 4$

Solution

In order to solve the problem, we first need to find each of the three variables. We can use the proportions the problem gives us to find the value of one part, and, by extension, the values of the variables (as $x$ would have $2$ parts, $y$ would have $3$, and $z$ would have $5$). One part, after some algebra, equals $10$, so $x$, $y$, and $z$ are $20$, $30$, and $50$, respectively.

We can plug $x$ and $y$ into the equation given to us: $30 = 20a-10$, and then solve to get $a = \boxed{\textbf{(A)}2}$.

See Also

1957 AHSME (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 9
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
All AHSME Problems and Solutions

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