Answer:
15 of the new members were girls.
Step-by-step explanation:
Ratio of boys to girls last year: 4:7. This means for every 4 boys, there were 7 girls.
Number of boys last year: Since the ratio is 4:7, we can't directly determine the number of boys last year without knowing the girls' numbers. However, we can express the number of boys as a multiple of 4 boys/girls unit. Let B_last_year represent the number of boys last year. Then, B_last_year = 4x, where x is the number of 4 boys/girls units.
Combined boys and girls last year: Similarly, let G_last_year represent the number of girls last year. Then, G_last_year = 7x.
Total members last year: The total number of members last year is B_last_year + G_last_year = 11x.
New members: 71 new members joined the club this year.
Total members this year: Adding new members, the total number of members this year is 11x + 71.
Ratio of boys to girls this year: 4:3. This means for every 4 boys, there are 3 girls.
Number of boys this year: We are given that there are 72 boys this year.
Expressing girls this year: Let G_this_year represent the number of girls this year. Then, G_this_year = 3y, where y is the number of 4 boys/3 girls units.
Combining boys and girls this year: The total number of members this year is 72 (boys) + 3y (girls) = 72 + 3y.
Equating total members: Since the total number of members should be the same last year and this year, we can set the equations from step 6 and 10 equal: 11x + 71 = 72 + 3y.
Solving for girls: Combine like terms and solve for y: 8x = 3y - 71. Divide both sides by 3: 8x/3 = y - 23.67. Round y up to the nearest whole number since we're dealing with the number of people: y ≈ 5.
Number of new girls: Since y represents the number of 4 boys/3 girls units, the actual number of new girls is 3y = 3 * 5 ≈ 15.
Therefore, approximately 15 of the new members were girls.
