There are 3 times as many boys as girls. If there are 24 more boys than girls, how many children are there altogether?

Question

Need help solving the question above.  Also need help with this one:

 

The total weight of Peter, David, and Henry is 123 kg.  Peter is 15kg heavier than David. David is 3 kg lighter than Henry.  Find Henry's weight.

 

Answer 1

Here's what we know:

b = 3g (There are three times as many boys as girl)

b = g + 24 (there are 24 more boys than girls)

 

Since both equations equal b, they also equal one another:

3g = g + 24

Subtract g from both sides:

2g = 24

Divide both sides by 2:

g = 12

 

b = 3 * 12

b = 36

 

check:

36 = 12 + 24

36 = 36

 

p + d + h = 123 (peter + david + henry's weight is 123 kg)

p = d + 15 (peter is 15 kg heavier than David)

d = h - 3 (david is 3 kg lighter than henry)

 

Now that we have values for our variables, let's plug them in:

(d + 15) + (h - 3) + h = 123

(h - 3) + 15 + h - 3 + h = 123

Combine like terms:

3h + 9 = 123

Subtract 9 from both sides:

3h = 114

Divide by 3:

h = 38

 

d = 38 - 3

d = 35

 

p = 35 + 15

p = 50

 

check:

50 + 35 + 38 = 123

123 = 123