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12 problems match “ratios”. Clear

Estimating fish population by capture-recapture ●○○○○ 10 ptsTo estimate the number of fish in a pond, $100$ fish were caught, tagged, and then released back into the pond. After some time, when the tagged fish had mixed completely with the rest of the fish, another $200$ fish were caught. If $10$ of them were tagged, estimate the total number of fish in the pond.
Cans of red paint in a mixture ●○○○○ 10 ptsPaint is to be mixed so that the ratio of red paint to white paint is $3$ to $2$ . If Ben wants to make $30$ cans of the mixture and all cans hold the same volume of paint, how many cans of red paint will he need?
Fair council representation by enrollment ●○○○○ 10 ptsThe 7th and 8th grades have enrollments of 520 and 650 students respectively. The two grades have a total of 18 representatives on the Student Council. Assuming representation is fair when the seats are allotted in proportion to enrollment, how many representatives should the 8th grade have?
Basketball players at a middle school ●○○○○ 10 ptsThe ratio of basketball players to football players at Roward Middle School is $2:7$ . There are 54 basketball and football players in total. How many basketball players are there?
Profit percent from pencil prices ●○○○○ 10 ptsThe cost price of 11 pencils is equal to the selling price of 10 pencils. Find the profit percent.
Distinct candy flavors by percent red ●●○○○ 20 ptsFour red candies and three green candies can be combined to make many different flavors. Two flavors are different if their percent red is different, so 3 red / 0 green is the same flavor as 2 red / 0 green, and 4 red / 2 green is the same flavor as 2 red / 1 green. If a flavor is made using some or all of the seven candies (at least one candy), how many different flavors are possible?
Fish population by tag and recapture ●●○○○ 20 ptsA biologist wants to estimate the number of fish in a lake. On May 1 she catches a random sample of 60 fish, tags them, and releases them. On September 1 she catches a random sample of 70 fish and finds that 3 of them are tagged. To estimate the number of fish in the lake on May 1, she assumes that 25% of the May 1 fish are no longer in the lake on September 1 (because of death and emigration), that 40% of the fish in the lake on September 1 were not in the lake on May 1 (because of births and immigration), and that the tagged and untagged fish in the September 1 sample are representative of the whole population. What number does she calculate for the number of fish in the lake on May 1?
Median of consecutive integer sets ●●○○○ 20 ptsLet $a$ , $b$ , and $c$ be integers with $a < b < c$ . Let $S$ be the set of all integers from $a$ to $b$ , inclusive, and $Q$ the set of all integers from $b$ to $c$ , inclusive. The median of $S$ is $\frac{3}{4}b$ and the median of $Q$ is $\frac{7}{8}c$ . Let $R$ be the set of all integers from $a$ to $c$ , inclusive. What fraction of $c$ is the median of $R$ ? Give your answer as a decimal.
Smallest survey size with given percentages ●●○○○ 20 ptsA total of $n$ people were asked a question in a survey. Exactly $76\%$ of the $n$ people responded "yes" and exactly $24\%$ of the $n$ people responded "no". What is the smallest possible value of $n$ ?
Boys to girls ratio from averages ●●○○○ 20 ptsIn a math test, the average score of a class is 78 points, and the average scores of the boys and the girls are 75.5 points and 81 points, respectively. Write the ratio of the number of boys to the number of girls in the class as $a:b$ in lowest terms. Find $a$ and $b$ .