A kiosk sells only salads and sandwiches and yesterday had 198 custom

Question

A kiosk sells only salads and sandwiches and yesterday had 198 customers, who each purchased either a salad, a sandwich, or both a salad and a sandwich. Yesterday, 40 percent of the items sold at the kiosk were sandwiches and 30 percent of the customers who purchased a sandwich also purchased a salad. How many of the customers purchased only a salad?

A. 90
B. 99
C. 108
D. 118
E. 120

Show Answer

Official Answer

C

A. 90
B. 99
C. 108
D. 118
E. 120

harjas2222 · Answer

this will use ratio i believe

sandwich:salad = 40:60 = 2x:3x

30% of those whose bought sandwich and salad = 0.3(2x)
 = 0.6x

Subtract salad 3x - 0.6x = 2.4x & 2x - 0.6x = 1.4x
 
Now 1.4x + 2.4x + 0.6x = 198
 4.4x = 198
 x= 45
Multiply 45 with 2.4x = 108 Ans

is it the right approach?

kevincan · Answer

Suppose N sandwiches were sold and thus 1.5N salads were sold

Since 30% of the N sandwiches were bought by customers who also bought a salad

0.7N customers bought only a sandwich
0.3N customers bought a sándwich and salad 
1.2N customers bought only a salad

Thus 1.2N of the 2.2N customers (6/11 of total) bought only a salad

6/11 of 198 = 108

kevincan · Answer

Alternatively , Suppose 0.4x sandwiches were sold and thus 0.6x salads were sold

Since 30% of the 0.4x sandwiches were bought by customers who also bought a salad

0.28x customers bought only a sandwich
0.12x bought a sándwich and salad
0.48x customers bought only a salad

Thus 0.48x of the 0.88x customers (6/11 of total) bought only a salad

6/11 of 198 = 108

kevincan · Answer

If x bought only a salad, 198 - x bought a sandwich . 0.3(198 -x) bought both .

198 - x is 40% of (1.3(198) - 0.3x)

Solve for x ( manageable but not fun )

kevincan · Answer

also , for every 100 items purchased

40 were sandwiches , 12 of which were puchased by people who also bought a salad. 
60 were salads , 12 of which were purchased by costumers who also bought a sandwich . The other 48 were purchased by customers who bought only a salad

Thus for every 88 customers , there were 48 customers who bought only a salad.

48/88 = 6/11
And 6/11 of 198= 108

A kiosk sells only salads and sandwiches and yesterday had 198 custom

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A kiosk sells only salads and sandwiches and yesterday had 198 custom

Prep Toolkit

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