Question

At a certain fast food restaurant, Brian can buy 3 burgers, 7 shakes, and one order of fries for Rs. 120 exactly. At the same place it would cost Rs. 164.5 for 4 burgers, 10 shakes, and one order of fries. How much would it cost for an ordinary meal of one burger, one shake, and one order of fries?

• A. Rs. 31
• B. Rs. 41
• C. Rs. 21
• D. Cannot be determined

Hint:

When two price combinations differ only in quantities of certain items, subtract equations to find partial sums.

Answer 1

The Correct Option is A

Let burger = $b$, shake = $s$, fries = $f$.
We have:
$3b + 7s + f = 120$ (1)
$4b + 10s + f = 164.5$ (2)
Subtract (1) from (2): $b + 3s = 44.5$.
We want $b + s + f$.
From (1): $b + s + f = 120 - (2s)$.
But from $b + 3s = 44.5$, $b = 44.5 - 3s$, so $b + s + f = (44.5 - 3s) + s + f = 44.5 - 2s + f$.
From (1): $3b + 7s + f = 120$, substituting $b$: $3(44.5 - 3s) + 7s + f = 120 \Rightarrow 133.5 - 9s + 7s + f = 120 \Rightarrow f - 2s = -13.5 \Rightarrow f = 2s - 13.5$.
Sub into $44.5 - 2s + f$: $44.5 - 2s + 2s - 13.5 = 31$.