There were some boys and girts at a camp. There were 2/3 as many girls as
boys. Each girl was given 2 chicken wings and each boy was given 3 chicken wings. In total, the children received 442 chicken wings altogether.
(a) How many boys were at the camp?
(b) How many chicken wings were given to the girls?
Let's start by using algebra to solve for the number of boys.
Let B be the number of boys and G be the number of girls. We know that:
G = (2/3)B (because there were 2/3 as many girls as boys)
Each girl received 2 chicken wings and each boy received 3 chicken wings, so the total number of chicken wings can be expressed as:
2G + 3B = 442
Now we can substitute the first equation (G = 2/3B) into the second equation:
2(2/3B) + 3B = 442
Simplifying:
4/3B + 3B = 442
7/3B = 442
B = 190
So there were 190 boys at the camp.
To find the number of chicken wings given to the girls, we can substitute this value for B into either of the two equations we used earlier:
G = (2/3)B = (2/3)(190) = 126
Therefore, there were 126 girls at the camp.
Each girl received 2 chicken wings, so the total number of chicken wings given to the girls is:
2G = 2(126) = 252
Therefore, 252 chicken wings were given to the girls.
Let's solve this problem step by step.
Step 1: Let's assume the number of boys at the camp is "B".
Step 2: Since there were 2/3 as many girls as boys, the number of girls at the camp would be 2/3 * B.
Step 3: Each girl was given 2 chicken wings, so the total number of chicken wings given to the girls would be 2 * (2/3 * B) = 4/3 * B.
Step 4: Each boy was given 3 chicken wings, so the total number of chicken wings given to the boys would be 3 * B.
Step 5: The total number of chicken wings given to all the children would be 4/3 * B + 3 * B = 442.
Step 6: Simplify the equation: 4/3 * B + 3 * B = 442.
- Multiply both sides of the equation by 3 to eliminate the fraction: 4 * B + 9 * B = 442 * 3.
- Simplify: 13 * B = 1326.
- Divide both sides of the equation by 13: B = 1326 / 13.
- Calculate: B ≈ 102.
(a) There were approximately 102 boys at the camp.
Step 7: Let's plug the value of B into the equation for the total number of chicken wings given to the girls: 4/3 * B.
- Calculate: 4/3 * 102 = 136.
(b) 136 chicken wings were given to the girls.