Two pizzas and four sandwiches cost $62.Four Pizzas and ten sandwiches cost $140.How much does each pizza and sandwich cost ?

The correct answer is: cost of one sandwich = $8

Complete step by step solution:
Let's denote the cost of one pizza =
And let the cost of one sandwich =
Let 2p + 4s = $62…(i)
and 4p+ 10s = $140….(ii)
On multiplying (i) with 2, we get 2( 2p + 4s = 62)
⇒4p + 8s = 124…(iii)
Now, we have the coefficients of p in (ii) and (iii) to be the same.
On subtracting (iii) from (ii),
we get LHS to be 4p + 10s-(4p + 8s) = 10s - 8s = 2s
and RHS to be 140 - 124 = 16
On equating LHS and RHS, we have 2s = 16
⇒ s = 8
On substituting the value of s in (i), we get 2p + 4 × 8 = 62

⇒ 2p + 32 = 62

⇒ 2p = 62 - 32

⇒ 2p = 30

⇒ p = 15
Hence we get  and y = 8
Hence cost of one pizza = $15
and cost of one sandwich = $8
Note: We can also solve these system of equations by making the coefficients of
to be the same in both the equations.