Question

# Ali, Ben and Carla made a total of 20 sandwiches. Ben made 3 times as many as Ali, and Carla made twice as many as Ben. How many sandwiches did Ali make? (A) 3(B) 4(C) 6(D) 2

Hint: First of all, we will have to read the question properly & then make equations accordingly. In such cases we need to consider their number of sandwiches individually. Then we will have to find a substitute value to find the result. Consider a variable for the number of sandwiches.

According to the question, If Ben made 3 times as many as Ali, then
$B = 3A$
And, if Carla made twice as many as Ben, then
$C = 2B$
Here, we are trying to find A, so let’s substitute the values earlier into solution.
So, according to the question,
$A + B + C = 20$
By substituting the values of B and C we get,
$\Rightarrow A + 3A + 2B = 20[\because B = 3A]$
$\Rightarrow A + 2A + 2\left( {3A} \right) = 20$ $\left[ {\because B = 3A} \right]$
Now we add the similar terms to get the value of A
$\Rightarrow A + 2A + 6A = 20$
$\Rightarrow 10A = 20$
$\Rightarrow A = 2$
Therefore the value of A = 2
Note: Alternative method: Let the sandwiches made by Ali be $x$.
As said in the question Ben made 3 times as many sandwiches as ali. So sandwiches made by Ben= $3x$.
Sandwiches made by Carla = $6x$. Given that the total sandwiches made were 20. $x+3x+6x$ = $20$.
$x$ = $2$.
So the total number of sandwiches made by Ali =$2$.