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svlad2 [7]
3 years ago
5

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.
Mathematics
2 answers:
Irina-Kira [14]3 years ago
6 0
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
leonid [27]3 years ago
6 0

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 brainly.com/question/3412497

2. A problem on angles 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.

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