Question

How to answer this question?

Answer 1

You can write two equations and solve a system of equations.

Let b = number of boys.

Let g = number of girls.

There are 40 students, so our first equation is:

b + g = 40

Each boy collected 80 kg, so all boys combined collected 80b.

Each girl collected 45 kg, so all girls combined collected 45g.

The total collected by all the students is 80b + 45g.

We are told the total collected was 2640 kg, so our second equation is:

80b + 45g = 2640

We have the system of equations

b + g = 40

80b + 45g = 2640

We will now solve it by the substitution method.

Solve the first equation for b:

b = 40 - g

Now substitute b with 40 - g in the second equation.

80b + 45g = 2640

80(40 - g) + 45g = 2640

3200 - 80g + 45g = 2640

3200 - 35g = 2640

-35g = -560

g = 16

Now we substitute g = 16 in the first original equation to find b.

b + g = 40

b + 16 = 40

b = 24

From our system of equations, we get that there are 24 boys and 16 girls.

Now we check the answer.

24 boys collect 24 * 80 kg = 1920 kg

16 girls collect 16 * 45 kg = 720 kg

All 40 students collect 1920 kg + 720 kg = 2640 kg.

2640 kg is indeed the number given to us by the problem, so our answer is correct.

Answer: There are 24 boys and 16 girls.

Answer 2

To solve this problem, we must set up a system of equations. Let's let b represent the number of boys collecting newspapers and g represent the number of girls collecting newspapers. Our first piece of information tells us that there are 40 students involved in the activity. This means that the sum of the boys and girls involved must be 40. In an equation, that is: b + g = 40. Our next equation involves the weight of the newspapers, 80 kg for boys and 45 kg for girls, where our total is 2640 kg of newspapers. This makes our second equation 80b + 45g = 2640.

Our system is as follows:

b + g = 40

80b + 45g = 2640

To solve this system, we are going to use substitution. To do this, we need to transform the first equation so that one variable is in terms of the other, as follows:

b + g = 40

b = 40 - g

Now that we have an equivalent value for the variable b, we can substitute this into the second equation so that this equation involves only one variable.

80(40 - g) + 45g = 2640

Now, we are going to use the distributive property to eliminate the parentheses.

3200 - 80g + 45 g = 2640

Now we are going to combine like terms on the left side of the equation.

3200 - 35g = 2640

Next, we are going to subtract 3200 from both sides of the equation to separate the constant and variable terms on opposite sides of the equation.

-35g = -560

Finally, we are going to divide both sides by -35 to get the variable g alone.

g = 16

This means that there were 16 girls involved in the activity. Next, we must substitute in this value for g into one of the original equations to solve for the other variable, b.

b + g = 40

b + 16 = 40

b = 24

Therefore, there were 24 boys involved in the activity and 16 girls involved in the activity.

Hope this helps!