Answer
Find out the how many of each were sold .
To prove
Let us assume that the number of hotdogs sold be x.
Let us assume that the number of hamburgers sold be y.
As given
The band boosters collected $2400 from the sale of hamburgers and hotdogs.
The amounts earned from hamburgers and hotdogs were equal.
A hamburger sold for $3 and a hot dog sold for $2 .
Thus the equation becomes
3y = 2x
2x + 3y = 2400
put 3y = 2x in the equation 2x + 3y = 2400.
2x + 2x = 2400
4x = 2400
x = 600
Put in the equation 2x + 3y = 2400.
2 × 600 + 3y = 2400
1200 +3y = 2400
3y = 2400 - 1200
3y = 1200
y = 400
Therefore the numbers of f hotdogs sold be 600 and the numbers of hamburgers sold be 400 .