help me with this

Question

A vendor sells pizza and soft drinks. A customer buys 7 slices of pizza and 5 drinks for $28.42. Another customer buys 6 slices of pizza and 4 drinks for $23.80. Find the cost of a slice of pizza.

Answer 1

Let P = cost of a slice of pzza and D = cost of a drink.

The equation from the first client is as follow:

7P + 5D = 28.42

The equation from the 2nd client is:

6P +4D = 23.80

 

The easiest way to solve this problem is probably via determinants to which you have probably not been exposed.

In my opinion the nex simples way is by elimination.

 

Multiply the first equation by 4 and the second equation by 5

28P + 20D = 113.68

30P + 20 D = 119

 

Subtract the 1st equation from the second

2P = 5.32 => P = 2.66

 

Sunstitue this value in the 1st equation

18.62 + 5D = 28.42

5D = 9.80 => D = 1.96

 

Put these 2 values into the 2nd equation to check.

Answer 2

7p + 5d = 28.42

6p + 4d = 23.80

 

Since we need to find p, we need the coeficients for d to be opposites so they cancel out. Multiplying an equation doesn't change the graph.

 

The LCM of 4 and 5 is 20.

 

4(7p + 5d) = 4(28.42)

-5(6p + 4d) = -5(23.80)

 

28p + 20d = 113.68

-30p - 20d = -119

 

Adding them together, we get...

 

-2p = -5.32

p = 2.66

 

One slice of pizza costs $2.66.

 

Answer 3

Set this up as a simultaneous system of 2 linear equations in 2 unknowns.

 

p = cost of pizza

d = cost of drink

 

7p + 5d = 28.42

6p + 4d = 23.80

 

Solve for p and d by elimination, matrix methods, or Cramer's rule.  You should get

 

p = $2.66

d = $1.96

 

Test the answers.