I need help on Word problem

Question

An order of three sodas and two hot dogs totaled $6.45, while the next order – five hot dogs and two sodas – was a $7.93 total.

How much for one hot dog and one soda?

Answer 1

This question involves solving simultaneous equations with 2 variables. Let x represent the cost of a soda and y = cost of a hotdog.

The problem then becomes : 3x + 2y = $6.45 and 2x + 5y = $7.93

Multiply each equation by a factor to eliminate one of the variables (in this case I chose x) then subtract the 2 equations

i) [3x + 2y = 6.45] x 2 => 6x + 4y = 12.90

ii) [2x + 5y = 7.93] x 3 => 6x + 15y = 23.79

Subtracting gives -11y = -10.89 Dividing both sides by -11 gives y = 0.99 or the cost of the hot dog = $0.99

Following how to solve simultaneous equations, chose one of the original equation (i) and substitute for y

gives 3x + 1.98 = 6.45 and solving for x gives x = 1.49; cost of soda = $1.49

Therefore cost of a soda and a hot dog = $1.49 + $0.99 =$2.48

All the best!