The money raised from each cookie sold will be $2.25, so this is to be multilplied by number of cookies \(\displaystyle x\) to obtain the revenue in terms of \(\displaystyle x\). Therefore, the revenue function is \(\displaystyle R(x)= 2.25x\).

Let \(\displaystyle x\) be the number of cookies sold. The Russian Club will need to spend 35 cents, or $0.35, per cookie for the ingredients, plus $350 flat for the ingredients, so the cost function will be

\(\displaystyle C(x) = 0.35x + 350\)

They will sell the cookies for $1.75 each, thereby earning a revenue of

\(\displaystyle R(x) = 1.75 x\)

They want to earn at least $800, so the profit \(\displaystyle P = R-C\) must be at least this - or

\(\displaystyle P (x) = R(x) - C(x) \ge 800\)

Replacing \(\displaystyle R(x)\) and \(\displaystyle C(x)\) with their definitions, the inequality becomes

\(\displaystyle 1.75 x- (0.35x + 350) \ge 800\)

Let \(\displaystyle x\) be the number of cookies sold. The Spanish Club will need to spend 75 cents, or $0.75, per cookie for the ingredients, plus $400 flat for the ingredients, so the cost function will be

\(\displaystyle C(x) = 0.75x + 400\)

They will sell the cookies for $2.50 each, thereby earning a revenue of

\(\displaystyle R(x) = 2.50 x\)

They want to earn at least $1,000, so the profit \(\displaystyle R-C\) must be at least this - or

\(\displaystyle P (x) = R(x) - C(x) \ge 1,000\)

Solve the inequality:

\(\displaystyle 2.50x - (0.75x+400)\ge 1,000\)

\(\displaystyle 1.75x - 400\ge 1,000\)

\(\displaystyle 1.75x \ge 1,400\)

\(\displaystyle 1.75x\div 1.75 \ge 1,400 \div 1.75\)

\(\displaystyle x \ge 800\)

The Spanish Club will need to sell 800 cookies.

Adam first buys 12 cell phones for $50 each, which means he spends:

12($50) = $600

He then sells the phones for $80 each, which means he earns:

12($80) = $960

The profit is the earnings minus the expenses, so Adam's profit is:

$960 - $600 = $360

The company makes an average net profit that is \(\displaystyle 35\%\) of the cost of building a machine. To calculate the average net profit in this case, simply do the following:

\(\displaystyle \$1549*0.35=\$542.12\)

So, to the nearest dollar, the company's net profit is \(\displaystyle \$$542\).

Note: avoid the trap answer \(\displaystyle \$543\). Our unrounded answer is \(\displaystyle \$542.12\), so we need to round down to \(\displaystyle \$$542\) instead of rounding up to \(\displaystyle \$543\).

A 55% increased of the unkown value \(\displaystyle X\) resulting as a \(\displaystyle +110,000\) increase can be written as follow \(\displaystyle X0.55= 110,000\).

So

\(\displaystyle X=\frac{110,000}{0.55}=\frac{110,000 \cdot 100}{55}\)

\(\displaystyle X=200,000\), which is the initial value.

To solve this problem, we simply have to multiply each position by their respective rate.

Note that we use a negative rate if the value decreased.

The final answer is then given by following equation 

\(\displaystyle 150,000\cdot0.04+120,000\cdot (-0.05)+45,000(0.01)\) and we end up with \(\displaystyle 450\).

To find the amount invested prior to the loss set up a proportion that represents what is given mathematically.

To write 60 percent of something is the same as,

\(\displaystyle 60\%\rightarrow \frac{60}{100}\)

If this is equivalent to $6,000 then the statement to solve would read,

\(\displaystyle \frac{60}{100}=\frac{\$6000}{Total\ Invested}\).

From here cross multiply and divide to solve for the amount invested prior to the loss.

\(\displaystyle \\ \$6000\times 100=60\times T \\ \$600000=60\times T \\ \\ \frac{\$600000}{60}=T \\ \\ \$10000=T\)