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PSYCHO15rus [73]
2 years ago
10

Brianna has x nickels and y pennies. She has no less than 20 coins worth no more

Mathematics
1 answer:
Bond [772]2 years ago
4 0

Answer:

y \ge 20 - x

y \le 80 -5x

(x,y) = (15,5)

Step-by-step explanation:

Given

Nickels = x

Pennies = y

Amount = \$0.80 maximum

Coins = 20 minimum

Required

Solve graphically

First, we need to determine the inequalities of the system.

For number of coins, we have:

x\ +\ y\ge 20 because the number of coins is not less than 20

For the worth of coins, we have:

0.05x\ +\ 0.01y\ \le0.80 because the worth of coins is not more than 0.80

So, we have the following equations:

x\ +\ y\ge 20

0.05x\ +\ 0.01y\ \le0.80

Make y the subject in both cases:

y \ge 20 - x

0.01y \le 0.80 - 0.05x

Divide through by 0.01

\frac{0.01y}{0.01} \le \frac{0.80}{0.01} -\frac{ 0.05x}{0.01}

y \le \frac{0.80}{0.01} -\frac{ 0.05x}{0.01}

y \le 80 -5x

The resulting inequalities are:

y \ge 20 - x

y \le 80 -5x

The two inequalities are plotted on the graph as shown in the attachment.

y \ge 20 - x --- Blue

y \ge 80 -5x --- Green

Point A on the attachment are possible solutions

At A:

(x,y) = (15,5)

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