Arithmetic › Ratio and proportion

Boys-to-girls ratios

Solve the first problem 18 problems

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1. 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?
2. Boys and total strength of a class ●○○○○ 10 ptsIn a class, $\frac{2}{3}$ of the students are boys and the rest, 17 students, are girls. (i) How many boys are in the class? (ii) What is the total number of students in the class?
3. 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?
4. Students who like to dance ●●○○○ 20 ptsOf the students attending a school party, $60\%$ are girls, and $40\%$ of the students like to dance. After these students are joined by $20$ more boys, all of whom like to dance, the party is now $58\%$ girls. How many students at the party now like to dance?
5. Scout troop after percentage growth ●●○○○ 20 ptsLast year, there were 30 more boys than girls in a scout troop. This year, the number of children in the troop increased by $10\%$, the number of boys increased by $5\%$, and the number of girls increased by $20\%$. How many children are in the troop this year?
6. 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 $b$.
7. Children with siblings in the class ●●●○○ 50 ptsIn a class, exactly 18 fathers and exactly 24 mothers attended a parent-teacher meeting, and at least one parent of each student attended. Exactly 10 boys and exactly 8 girls had both parents present. For exactly 4 boys and exactly 3 girls only the mother was present, and for exactly 1 boy and exactly 1 girl only the father was present. There are no children in the class with step-parents or step-siblings. Determine the number of children in this class who have siblings in the same class.

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