Question

A vendor sells pizza and soft drinks. A customer buys 6 slices of pizza and 5 drinks for $31.60. Another customer buys 5 slices of pizza and 4 drinks for $26.02. Find the cost of a slice of pizza.

Answer 1

let the price of a slice of pizza be 'p' and that of soft drink be 's'

   6 p + 5 s = 31.60............equation (i)
   5 p + 4 s = 26.02............equation (ii)

6 p + 5 s = 31.60............×4
5 p + 4 s = 26.02............×5

24 p + 20 s = 126.4
25 p + 20 s = 130.1

p = 3.7

   Answer = 3.7 Dollars

Answer 2

The cost of a slice of pizza is $\boxed{\ 3.7}$.

Further explanation:

Given:

A vendor sells soft drinks and pizza.

A customer came and buys $6$ slices of pizza and also buys $5$ soft drinks and the total cost for that customer is $\ 31.60$.

Another customer came and buys $5$ slices of pizza and also buys $4$ soft drinks and the total cost for that customer is $\ 26.02$.

The objective is to find the cost of a slice of pizza.

Consider the cost of the pizza to be $x$ dollars and the cost of soft drinks be $y$ dollars.

Given that a customer buys $6$ slices of pizza and $5$ soft drinks and this costs $\ 31.60$, so this can be written in the form of an equation as follows:

$\fbox{\begin\\\ \math 6x+5y=31.60\\\end{minispace}}$     ....(1)

Another customer buys $5$ slices of pizza and $4$ soft drinks and this costs $\ 26.03$, so this can be written in the form of an equation as follows:

$\fbox{\begin\\\ \math 5x+4y=26.02\\\end{minispace}}$     ....(2)

Now, we have to solve both the equations (1) and (2) to find the cost of pizza.

Multiply equation (1) by 4 as follows:

$4(6x+5y)=4\times31.60\\24x+20y=126.4$

Label the above equation as follows:

$\boxed{24x+20y=126.4}$    .....(3)

Multiply equation (2) by 5 as follows:

$5(5x+4y)=5\times26.02\\25x+30y=130.1$

Label the above equation as follows:

$\boxed{25x+30y=130.1}$   .......(4)

To find the value of $x$ subtract equation (3) from equation (4) as shown below:

$\begin{aligned}25x+20y-(24x+20y)&=130.1-126.4\\25x+20y-24x-20y&=3.7\\x&=3.7\end{aligned}$

Therefore, the value of $x$ is $3.7$.

Thus, the cost of one slice of pizza is $\boxed{\ 3.7}$.

Learn more:

1. A problem on linear equation https://brainly.com/question/3412497

2. A problem on angles https://brainly.com/question/3413207

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations in two variables

Keywords: Vendor, pizza, soft drinks, customer, slices, $31.60, $26.02, cost, linear, equation, solve, multiply, subtract, linear equation, variable.