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galina1969 [7]
2 years ago
5

A home is to be built on a 56 foot 9 inch wide lot. The house is 5 feet 5 inches from the side of the lot and is 34 feet 10 inch

es wide. How far is the house from the other side of the lot ?
Mathematics
1 answer:
ch4aika [34]2 years ago
8 0

Answer:

=16 ft 6 in

Step-by-step explanation:

Remainder side = Total lot - house -other side

=(56 ft 9 in) - (34 ft 10 in) - (5 ft 5 in)

=(55 ft 21 in) - (34 ft 10 in) - (5 ft 5 in)

=16 ft 6 in

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The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find
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Answer:

x = 10. In other words, there number of girls is 10.

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}.

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\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}.

For this question:

\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}.

\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}.

Therefore:

\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}.

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\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}.

From the question, this average should be equal to 123. In other words:

\displaystyle \frac{1875 + 120\, x}{15 + x} = 123.

Solve this equation for x to obtain:

1875 + 120\, x= 123\, (15 + x).

(123 - 120)\, x = 1875 - 123 \times 15.

x = 10.

In other words, the number of girls here is 10.

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