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$A unicorn daycare center requires there to be 2 supervisors for every 18 baby unicorns. Write an equation that shows the relationship between n, the number of supervisors, and u, the number of baby unicorns. Please note that this is a magical daycare center, so fractional supervisors are allowed.$

A unicorn daycare center requires there to be $2$ supervisors for every $18$ baby unicorns. $\newline$ Write an equation that shows the relationship between $n$ , the number of supervisors, and $u$ , the number of baby unicorns. $\newline$ Please note that this is a magical daycare center, so fractional supervisors are allowed.

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Solve a system of equations using substitution: word problems

Full solution

Q. A unicorn daycare center requires there to be

2

supervisors for every

18

baby unicorns.

\newline

Write an equation that shows the relationship between

n

, the number of supervisors, and

u

, the number of baby unicorns.

\newline

Please note that this is a magical daycare center, so fractional supervisors are allowed.

Determine Ratio: Determine the ratio of supervisors to baby unicorns. The problem states that there are $2$ supervisors for every $18$ baby unicorns. This gives us a ratio of supervisors to baby unicorns.
Write Equation: Write the equation using the ratio. $\newline$ Since $2$ supervisors are needed for $18$ baby unicorns, we can write the equation as $\frac{n}{u} = \frac{2}{18}$ . This equation represents the ratio of supervisors to baby unicorns.
Simplify Ratio: Simplify the ratio. $\newline$ The ratio $\frac{2}{18}$ can be simplified by dividing both the numerator and the denominator by $2$ . This gives us $\frac{1}{9}$ . So, the simplified ratio is $\frac{n}{u} = \frac{1}{9}$ .
Rearrange Equation: Rearrange the equation to solve for $n$ . To find the relationship between $n$ and $u$ , we need to solve for $n$ . Multiplying both sides of the equation by $u$ gives us $n = \frac{1}{9} \times u$ .
Check Equation: Check the equation. $\newline$ The equation $n = \frac{1}{9} \times u$ means that for every unicorn, there is $\frac{1}{9}$ of a supervisor. Since the problem allows for fractional supervisors, this equation is correct.

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