Question

Mario, Franco and Gina share 153 badges in the ratio 2:3:4. Calculate how many badges Mario gets.

Answer 1

Hint: Here we will let the ratio of Mario, Franco and Gina as 2x, 3x and 4x respectively and add them and equate them equal to total number of badges to get the value of x and then finally find the number of badges Mario gets.

Complete step-by-step answer:
Let the ratio of Mario be 2x
Let the ratio of Franco be 3x
Let the ratio of Gina be 4x
Now it is given that total number of badges are 153
Hence,
\[2x + 3x + 4x = 153\]
Solving for x we get:-
\[9x = 153\]
Dividing by 9 we get:-
\[x = \dfrac{{153}}{9}\]
\[ \Rightarrow x = 17\]
Now since the share of Mario is 2x
Hence putting the value of x we get:-
\[{\text{share of Mario}} = 2 \times 17\]
Solving it we get:-
\[{\text{share of Mario}} = 34{\text{badges}}\]

Hence Mario gets 34 badges.

Note: An alternative method to solve this problem is:-
Let us calculate the share of each of the three persons.
Hence, share of Mario is given by:-
\[{\text{share of Mario}} = \dfrac{2}{{2 + 3 + 4}} \times {\text{ total badges}}\]
Solving it further and putting the respective value we get:-
\[{\text{share of Mario}} = \dfrac{2}{9} \times {\text{ 153}}\]
Simplifying it we get:-
\[{\text{share of Mario}} = 2 \times 17\]
Solving it we get:-
Hence Mario gets 34 badges.