Question

Anna has I nickels and y dimes. She has at most 22 coins worth a minimum of $1.40combined. Solve this system of inequalities graphically and determine one possiblesolution.Inequality 1:yplastInequality 2: y2plot882624NO1816141210864202 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40Anna could havenickels anddimes.Submit Answer

Answer 1

Here, there are x nickels and y dimes

At most, they are 22 in number;

Mathematically;

x + y ≤ 22

y ≤ 22 - x

The above is the first inequality

A nickel is worth 5 cents while a dime is worth 10 cents

So the worth of x nickels is 5x cents

The worth of y dimes is 10y cents

Kindly note that $1.40 is same as 140 cents

So the sum of both is at least 140 cents

5x + 10y ≥ 140

10y ≥ 140 - 5x

Now divide both sides by 10

y ≥ 14 - 0.5x

So the two inequalities to solve simultaneously are;

y ≤ 22 - x and y ≥ 14 - 0.5x