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

Answer 1

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.

Complete step-by-step answer:
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
Hence, Ali made 2 sandwiches.
So the correct answer is D

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= $3x$.
Carla made twice as many as Ben.
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 =$2$.
We used the concept of linear equations in one variable in the alternative method.