Question

Evan has x pennies and y nickels. He has no less than 20 coins worth no more than $0.75 combined. Solve thus system of inequalities graphically and determine onr possible solution

Answer 1

Answer:

$x$ = 12, $y$ = 10

Step-by-step explanation:

Given that:

Number of pennies = $x$

Total amount in pennies = $x$ cents

Number of nickels = $y$

Total amount in nickels = 5$y$ cents

Number of coins are not less than 20.

i.e. the inequality can be written as:

$x+y>20 .... (1)$

Total money is not more than $0.75 i.e. 75 cents

The inequality can be written as:

$x+5y$ ...... (2)

Also, the number of nickels and pennies must be in positive numbers.

Therefore,  

$x > 0 ...... (3)\\y > 0 ....... (4)$

When plotted in graph, we get the image as attached in the answer area.

Solution of the graph is the area which is common to both the lines.

And one solution between them is (12, 10)

i.e. number of pennies, $x$ = 12

Number of nickels, $y$ = 10