QUARTER FINAL
2013
Presbyterian Boys SHS
Wesley Girls SHS
St Augustine's College
QUESTION
$Z$ varies directly as $X$ and inversely as $Y$. If $Z=40$ when $X=100, Y=20$, find $Z$ when $X=50, Y=40$.
ANSWER: $10$
SOLUTION
$Z = \dfrac{kX}{Y}$
$k = \dfrac{ZY}{X}$
$k = \dfrac{40(20)}{100}$
$k = 8$
$Z = \dfrac{8(50)}{40}$
$Z = 10$
PRACTICE QUESTIONS
1. $Z$ varies directly as $X$ and inversely as $Y$. If $Z=18$ when $X=12$, $Y=4$, find $Z$ when $X=20$, $Y=8$.
ANSWER: $15$
SOLUTION
Write the variation equation:
$Z=k\dfrac{X}{Y}$
Find $k$ using $Z=18$, $X=12$, $Y=4$:
$18=k\times\dfrac{12}{4}$
$18=k\times\dfrac{12}{4}$
$k=6$
Find $Z$ when $X=20$ and $Y=8$:
$Z=6\times\dfrac{20}{8}$
$Z=15$
2. $Z$ varies directly as $X$ and inversely as $Y$. If $Z=20$ when $X=8$, $Y=2$, find $Z$ when $X=12$, $Y=6$.
ANSWER: $10$
SOLUTION
Write the variation equation:
$Z=k\dfrac{X}{Y}$
Find $k$ using $Z=20$, $X=8$, $Y=2$:
$20=k\times\dfrac{8}{2}$
$20=k\times\dfrac{8}{2}$
$k=5$
Find $Z$ when $X=12$ and $Y=6$:
$Z=5\times\dfrac{12}{6}$
$Z=10$
3. $Z$ varies directly as $X$ and inversely as $Y$. If $Z=12$ when $X=20$, $Y=5$, find $Z$ when $X=9$, $Y=3$.
ANSWER: $9$
SOLUTION
Write the variation equation:
$Z=k\dfrac{X}{Y}$
Find $k$ using $Z=12$, $X=20$, $Y=5$:
$12=k\times\dfrac{20}{5}$
$12=k\times\dfrac{20}{5}$
$k=3$
Find $Z$ when $X=9$ and $Y=3$:
$Z=3\times\dfrac{9}{3}$
$Z=9$
4. $Z$ varies directly as $X$ and inversely as $Y$. If $Z=20$ when $X=6$, $Y=3$, find $Z$ when $X=15$, $Y=5$.
ANSWER: $30$
SOLUTION
Write the variation equation:
$Z=k\dfrac{X}{Y}$
Find $k$ using $Z=20$, $X=6$, $Y=3$:
$20=k\times\dfrac{6}{3}$
$20=k\times\dfrac{6}{3}$
$k=10$
Find $Z$ when $X=15$ and $Y=5$:
$Z=10\times\dfrac{15}{5}$
$Z=30$
5. $Z$ varies directly as $X$ and inversely as $Y$. If $Z=12$ when $X=15$, $Y=5$, find $Z$ when $X=18$, $Y=6$.
ANSWER: $12$
SOLUTION
Write the variation equation:
$Z=k\dfrac{X}{Y}$
Find $k$ using $Z=12$, $X=15$, $Y=5$:
$12=k\times\dfrac{15}{5}$
$12=k\times\dfrac{15}{5}$
$k=4$
Find $Z$ when $X=18$ and $Y=6$:
$Z=4\times\dfrac{18}{6}$
$Z=12$
6. $Z$ varies directly as $X$ and inversely as $Y$. If $Z=6$ when $X=5$, $Y=10$, find $Z$ when $X=8$, $Y=4$.
ANSWER: $24$
SOLUTION
Write the variation equation:
$Z=k\dfrac{X}{Y}$
Find $k$ using $Z=6$, $X=5$, $Y=10$:
$6=k\times\dfrac{5}{10}$
$6=k\times\dfrac{5}{10}$
$k=12$
Find $Z$ when $X=8$ and $Y=4$:
$Z=12\times\dfrac{8}{4}$
$Z=24$