A candle shop sells scented candles for $16 each and unscented candles for $10 each. The shop sells 28 candles today and makes $
1 answer:
<h3><u>The system of linear equations that represents the situation is:</u></h3>
a + b = 28
16a + 10b = 400
<h3><u>20 scented candles and 8 unscented candles were sold</u></h3><em><u>Solution:</u></em>
Let "a" be the number of scented candles sold
Let "b" be the number of unscented candles sold
From given,
Cost of 1 scented candles = $ 16
Cost of 1 unscented candles = $ 10
<em><u>The shop sells 28 candles today</u></em>
Therefore,
a + b = 28
b = 28 - a ------- eqn 1
<em><u>The shop sells 28 candles today and makes $400</u></em>
Therefore,
number of scented candles sold x Cost of 1 scented candle + number of unscented candles sold x Cost of 1 unscented candles = 400
16a + 10b = 400 ------ eqn 2
<em><u>Substitute eqn 1 in eqn 2</u></em>
16a + 10(28 - a) = 400
16a + 280 - 10a = 400
6a = 400 - 280
6a = 120
a = 20
<em><u>Substitute a = 20 in eqn 1</u></em>
b = 28 - 20
b = 8
Thus 20 scented candles and 8 unscented candles were sold
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Answer:
Question 1) 17.4
Question 2) 1.7
Question 3) 2.8
Question 4) 8.6
Step-by-step explanation:
Mean absolute deviation is the average distance between the data points from the set to the mean point of the data set. It shows the variability in data or how much the data points are spread.
method to calculate Mean absolute deviation:
a. calculate mean
b. calculate absolute deviation of each data point
c. add all the deviations
d. divide absolute deviation by number of points
mean absolute deviation = ∑l-xl / n
The given problem has four sub-parts
Solution 1:
Mean= (78+99+90+80+55+56+102+88+60+42)/10
= 750/10
= 75
Mean absolute deviation= ( I 78-75 I + I 99-75 I+I 90-75 I + I 80-75 I +
I 55-75 I + I 56-75 I + I 102-75 I + I 88- 75 I +
I 60-75 I + I 42-75 I) /10
= (174)/10
= 17.4
Solution 2:
Mean = (10+13+7+12+9+8+12+10+11+13)/10
= (105)/10
= 10.5
Mean absolute deviation = ( I 10-10.5 I + I 13-10.5 I + I 7-10.5 I + I 12-10.5 I +
I 9-10.5 I + I 8-10.5 I + I 12-10.5 I + I 10-10.5 I +
I 11-10.5 I + I 3-10.5 I) /10
= 17/10
= 1.7
Solution 3:
Mean= (1+7+10+5+3+3+6+12+9+4)/10
= 60/10
= 6
Mean absolute deviation = ( I 1-6 I + I 7-6 I + I 10-6 I + I 5-6 I + I 3-6 I +
I 3-6 I + I 6-6 I + I 12- 6 I + I 9-6 I + I 4-6 I) /10
= (28)/10
= 2.8
Solution 4:
Mean= (30+46+25+45+18+25+15+32+40+24)/10
= 300/10
= 30
Mean absolute deviation = ( I 30-30 I + I 46-30 I + I 25-30 I + I 45-30 I +
I 18-30 I + I 25-30 I + I 15-30 I + I 32-30 I +
I 40-30 I + I 24-30 I) /10
= (86)/10
= 8.6
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