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Nata [24]
3 years ago
15

Solve.

Mathematics
1 answer:
Grace [21]3 years ago
8 0

Answer:

Total bikes and cars are 260

Step-by-step explanation:

<u>Cars</u>: n_{cars}185

<u>Bikes</u>: n_{bikes}=n_{cars}-113=72

<u>Total</u>: n_{total}=n_{bikes}+n_{cars}=257

Rounding to the nearest ten: 260

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Let’s pretend that we want to give our employees in total a28% raise in the next two years, but we want to spread out aconsisten
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Solution

- The solution steps are given below:

\begin{gathered} \text{ Let the original amount be X} \\  \\ \text{ If we want a 28\% raise over the next two years, then it means that the amount will be:} \\ X+\frac{28}{100}X=1.28X \\  \\ \text{ If we want to give them a consistent raise each year, we can compute the scenario as follows:} \\ \text{ Let the percentage be }y \\  \\ X+y\%\text{ of }X=\text{ Salary after first year} \\  \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)\text{ = Salary after second year.} \\  \\ \text{ But we already know that the salary after second year is }1.28X \\ \text{ Thus, we can say:} \\ (X+y\%\text{ of }X)+y\%\text{ of }(X+y\%\text{ of }X)=1.28X \\  \\ \text{ Simplifying, we have:} \\ X+\frac{yX}{100}+\frac{y}{100}(X+\frac{yX}{100})=1.28X \\  \\ \text{ Divide through by }X \\ 1+\frac{y}{100}+\frac{y}{100}(1+\frac{y}{100})=1.28 \\  \\ \text{ Subtract 1 from both sides and expand the brackets} \\ \frac{y}{100}+\frac{y}{100}+(\frac{y}{100})^2=1.28-1=0.28 \\  \\ \frac{2y}{100}+(\frac{y}{100})^2=0.28 \\  \\ \text{ Multiply both sides by }100^2 \\ 200y+y^2=2800 \\  \\ \text{ Rewrite, we have:} \\ y^2+200y-2800=0 \\  \\ Solving\text{ the equation using the Quadratic formula, we have that:} \\ y=\frac{-200\pm\sqrt{200^2-4(-2800)}(1)}{2(1)} \\  \\ y=-213.137\text{   or   }13.137 \\  \\ \text{ Since the change in salary is an increase, thus, the rate }y\text{ has to be positive.} \\ \text{ Thus, } \\ y=13.137\approx13.14\% \\  \\  \end{gathered}

Final Answer

y = 13.14%

The screenshots of the solution are:

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Step-by-step explanation:

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