Welcome to your ACT 1 Alg: Represent direct and inverse variation

$Q_{1}:$ An inverse variation is an equation of the form

$Q_{2}:$ A direct variation variation is an equation of the form

$Q_{3}:$ If $y$ varies directly as $x$ , and $y = 4$ when $x = 6$ , find $y$ when $x = 18$ .

$Q_{4}:$ If $w$ varies inversely as $x$ , and $w =\frac{1}{3}$ when $x = 15$, find $w$ when $x = 25$.

$Q_{5}:$ Which of the following tables shows a relationship in which $y$ is directly proportional to $ x $?

$Q_{6}:$ The distance it takes an automobile to stop varies directly as the square of its speed. If the stopping distance of a car traveling at $40 mph$ is $320 feet$, what is the stopping distance of a car traveling at $50mph$?

Hint

$Q_{7}:$ If $y$ varies inversely as $\sqrt{x}$ , and $y = 12$ when $x = 16 $, what is the value of $y$ when $x = 100 $?

Hint

$Q_{8}:$ If $4$ bottles of milk cost $2£$, how many bottles of milk can you buy for $8£$?

Hint

$Q_{9}:$ If $b$ boys can deliver $n$ newspapers in one hour, how many newspapers can $c$ boys deliver in the same time?

Hint

$Q_{10}:$ Find the cost of $8$ books if $3$ books of the same kind cost $D$ jd.

Hint

$Q_{11}:$ On a map $\frac{1}{2}$inch $= 10$ miles. How many miles apart are two towns that are $2.25$ inches apart on the map?

$Q_{12}:$ The toll on the Intercoastal Thruway is $8$ cents for every $5$ miles traveled. What is the toll for a trip of $115$ miles on this road?

Hint

$Q_{13}:$ Malik’s car uses $20$ gallons of gas to drive $425$ miles. At this rate, approximately how many gallons of gas will he need for a trip of $1000$ miles?

$Q_{14}:$ If $r$ planes can carry $p$ passengers, how many planes are needed to carry $m$ passengers?

$Q_{15}:$ If $3$ men can paint a house in $2$ days, how long will it take $2$ men to do the same job?

$Q_{16}:$ A field can be plowed by $8$ machines in $6$ hours. If $3$ machines are broken and cannot be used, how many hours will it take to plow the field?

$Q_{17}:$ Camp Starlight has enough milk to feed $90$ children for $4$ days. If $10$ of the children do not drink milk, how many days will the supply last?

$Q_{18}:$ A pulley revolving at $200$ revolutions per minute has a diameter of $15$ inches. It is belted to a second pulley which revolves at $150$ revolutions per minute. Find the diameter, in inches, of the second pulley.

$Q_{19}:$ Two girls weighing $60$ pounds and $80$ pounds balance a seesaw. How many feet from the fulcrum must the heavier girl sit if the lighter girl is $8$ feet from the the fulcrum?

$Q_{20}:$A gear with $20$ teeth revolving at $200$ revolutions per minute is meshed with a second gear turning at $250$ revolutions per minute. How many teeth does this gear have?

$Q_{21}:$ A farmer has enough chicken feed to last $30$ chickens for $4$ days. If $10$ more chickens are added, how many days will the feed last?

$Q_{22}:$ At $c$ cents per can, what is the cost of $p$ cases of soda if there are $12$ cans in a case?

$Q_{23}:$ If $m$ boys can put up a fence in $d$ days, how many days will it take to put up the fence if two of the boys cannot participate?

$Q_{24}:$ A recipe calls for $\frac{3}{4}$ lb. of butter and $18$ oz. of sugar. If only $10$ oz. of butter are available, how many ounces of sugar should be used?

$Q_{25}:$ If $3$ kilometers are equal to $1.8$ miles, how many kilometers are equal to $100$ miles?