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Answer to Q124

Nine men went to a restaurant. Eight of them spent $6 each for their meals and the ninth man spent $4 more than the average expenditure of all nine men. What is the average expenditure?

Average simply is the sum of a set of data divided by the quantity of the data.

We know what 8 men spent which is $6 each
Let what the ninth man spent be = Y
Let the average of what the nine men spent be = Z

the ninth man spent $4 more than the average expenditure of all nine men

So, Y = Z + 4 (eqn 1)

average of what all nine men spent will then be
((6 x 8) + Y) ÷ 9 = Z
(48 + Y) ÷ 9 = Z

Multiply all through by 9
48 + Y = 9Z (eqn 2)

Put eqn 1 into eqn 2
48 + Z + 4 = 9Z
52 + Z = 9Z
52 = 9Z - Z
52 = 8Z
Z = 52 ÷ 8
Z = 6.5

So, average of the expenditure is $6.5

Answer: $6.5

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537 viewsFeb 4, 2021 at 12:07

Answer to Q124

Nine men went to a restaurant. Eight of them spent $6 each for their meals and the ninth man spent $4 more than the average expenditure of all nine men. What is the average expenditure?

Average simply is the sum of a set of data divided by the quantity of the data.

We know what 8 men spent which is $6 each
Let what the ninth man spent be = Y
Let the average of what the nine men spent be = Z

the ninth man spent $4 more than the average expenditure of all nine men

So, Y = Z + 4 (eqn 1)

average of what all nine men spent will then be
((6 x 8) + Y) ÷ 9 = Z
(48 + Y) ÷ 9 = Z

Multiply all through by 9
48 + Y = 9Z (eqn 2)

Put eqn 1 into eqn 2
48 + Z + 4 = 9Z
52 + Z = 9Z
52 = 9Z - Z
52 = 8Z
Z = 52 ÷ 8
Z = 6.5

So, average of the expenditure is $6.5

Answer: $6.5

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