Anthony has been saving nickels (N), dimes (D), and quarters (Q) over the last year. He knows that he has twice as many nickels as quarters. When he takes the coins to the change machine to exchange them for paper money, he learns that he has 260 coins that total $29.75. Determine the number of each type of coin Anthony saved.

75 number of quarters

150 number of nickels

35 number of dimes

Step-by-step explanation:

Let x, y and z be the amount of quarters, nickel and dimes respectively.

he learns that he has 260 coins, thus;

x + y + z = 260 - - - (1)

Now, we are told that he has twice as many nickels as quarters.

Thus, number of nickels = 2x

y = 2x - - - (2)

From online research, we have the following cost;

1 quarter = $0.25

1 nickel = $0.05

1 dime = $0.1

Total cost is $29.75. Therefore;

0.25x + 0.05y + 0.1z = 29.75 - - - (3)

Put 2x for y in eq (1) and eq (3) to get;

x + 2x + z = 260

3x + z = 260 - - - (eq 4)

0.25x + 0.05(2x) + 0.1z = 29.75

0.25x + 0.10x + 0.1z = 29.75

0.35x + 0.1z = 29.75 - - - (eq 5)

From eq(4), z = 260 - 3x

Thus;

0.35x + 0.1(260 - 3x) = 29.75

0.35x + 26 - 0.3x = 29.75

0.05x = 29.75 - 26

0.05x = 3.75

x = 3.75/0.05

x = 75

So, z = 260 - 3(75)

z = 260 - 225

z = 35

Since y = 2x,

Then,y = 2(75) = 150

Thus,we have;

75 number of quarters

150 number of nickels

35 number of dimes

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

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