At a concert, two-fifths of the people were men. There were three times as many women as children. If there were 45 more men than children, how many people were at the concert?
Answer (2)
x − a ll p eo pl e 5 2 x − m e n 5 2 x − 45 − c hi l d re n 3 ( 5 2 x − 45 ) − w o m e n x = 5 2 x + ( 5 2 x − 45 ) + ( 3 ( 5 2 x − 45 )) ∣ m y lt i pl y b y 5 5 x = 2 x + 2 x − 225 + 6 x − 675 5 x = 10 x − 900 ∣ s u b t r a c t 10 x − 5 x = − 900 ∣ d i v i d e b y − 5 x = 180 T h ere w ere 180 p eo pl e a t co n cer t .
There were 180 people at the concert. This was determined by setting up equations based on the information about men, women, and children at the concert and solving for the total number. The calculations involved relationships between the numbers of each group of attendees.
;
