\(\displaystyle -(x-45)\) is the opposite of \(\displaystyle x-45\), which is the difference of a number and forty-five; therefore, \(\displaystyle -(x-45)\) is the opposite of the difference of a number and forty-five.

\(\displaystyle -x - 65\) is sixty-five subtracted from \(\displaystyle -x\), which is the opposite of a number; therefore, \(\displaystyle -x - 65\) is "sixty-five subtracted from the opposite of a number."

\(\displaystyle \left ( y - 34\right ) ^{2}\) is the square of \(\displaystyle y - 34\), which is the difference of a number and thirty-four. Therefore, \(\displaystyle \left ( y - 34\right ) ^{2}\) is the difference of a number and thirty-four. 

Let x be the original price.  If the original price was given a discount, the value of the percent discount must be subtracted from the original price.

\(\displaystyle x- \frac{99}{100}x = $1.25\)

\(\displaystyle .01x = 1.25\)

\(\displaystyle x=\frac{1.25}{.01}= $125\)

\(\displaystyle \frac{1}{5 - x}\) is the reciprocal of \(\displaystyle 5 - x\), which is the difference of five and a number. Therefore, \(\displaystyle \frac{1}{5 - x}\) is "the reciprocal of the difference of five and a number".

Let \(\displaystyle x\) be the number of dimes. Then there are \(\displaystyle 64-x\) nickels.

An equation can be set up and solved for \(\displaystyle x\) for the amount of money:

\(\displaystyle 0.10x + 0.05 (64-x) = 5.15\)

\(\displaystyle 0.10x + 0.05 \cdot 64-0.05 \cdot x = 5.15\)

\(\displaystyle 0.10x-0.05 x + 3.2 = 5.15\)

\(\displaystyle 0.05 x + 3.2 = 5.15\)

\(\displaystyle 0.05 x + 3.2 - 3.2 = 5.15 - 3.2\)

\(\displaystyle 0.05 x = 1.95\)

\(\displaystyle 0.05 x \div 0.05= 1.95 \div 0.05\)

\(\displaystyle x = 39\), the number of dimes.

Eight large cappucinos will cost Greg

\(\displaystyle \$3.89 \times 8 = \$31.12\).

This leaves him 

\(\displaystyle \$80.00 - \$31.12 = \$ 48.88\)

to buy croissants, which cost \(\displaystyle \$2.29\).

Let \(\displaystyle X\) be the number of croissants he buys. Then

\(\displaystyle 2.29 X \leq48.88\)

\(\displaystyle X \leq48.88 \div 2.29 \approx 21.3\)

Greg can buy up to 21 croissants.

Let \(\displaystyle N\) be the number of pizzas made and sold. Each pizza will require $2 worth of ingredients, so the ingredients in total will cost \(\displaystyle 2N\). Add this to the cost to rent the equipment and the cost will be \(\displaystyle 2N + 250\).

The pizzas will cost $4.50 each, so the money raised will be \(\displaystyle 4.5N\).

The profit will be the difference between the revenue and the cost:

\(\displaystyle 4.5 N - \left (2N + 250 \right )\)

The French club wants a profit of at least $500, so we set up and solve the inequality:

\(\displaystyle 4.5 N - \left (2N + 250 \right ) \geq 500\)

\(\displaystyle 4.5 N - 2N - 250 \right ) \geq 500\)

\(\displaystyle 2.5 N - 250 \geq 500\)

\(\displaystyle 2.5 N \geq 750\)

\(\displaystyle N \geq 750 \div 2.5\)

\(\displaystyle N \geq 300\)

At least 300 pizzas must be made and sold.

The number of pounds of coffee beans totals 50, so one of the equations would be

\(\displaystyle x + y = 50\).

The total price of the Kona beans is the unit price, $24 per pound, multiplied by the quantity, \(\displaystyle x\) pounds. This is \(\displaystyle 24x\) dollars. Similarly, the total price of the Ethiopian delight beans is \(\displaystyle 10y\) dollars, and the price of the mixture is \(\displaystyle 14.20 \times 50 = 710\) dollars. Add the prices of the Kona and Ethiopian Delight beans to get the price of the mixture:

\(\displaystyle 24x + 10 y = 710\)

These are the equations of the system.

Since Leslie has twice as many dimes as nickels, the number of nickels she has is half the number of dimes, or half of \(\displaystyle D\). This means she has \(\displaystyle \frac{1}{2}D\) nickels. Also, since she has four more quarters than dimes, she has \(\displaystyle D + 4\) quarters.

She has

\(\displaystyle \$0.05 \times \frac{1}{2}D = \$0.025 D\) in nickels,

\(\displaystyle \$0.10 D\) in dimes, and

\(\displaystyle \$0.25 \cdot (D+4) = \$0.25 \cdot D+\$0.25 \cdot 4 = \$0.25 D+\$1.00\) in quarters.

In total, the number of dollars Leslie has is

\(\displaystyle 0.025 D + 0.10D + 0.25D+ 1.00\)

\(\displaystyle = \left (0.025 + 0.10 + 0.25 \right ) D+ 1\)

\(\displaystyle = 0.375 D+ 1\)

Leslie has \(\displaystyle 0.375 D+ 1\) dollars.