All of the houses on Algebra Avenue in Mathopolis are either two or three stories high. The Mathemagician assures you that the total number of stories on Algebra Avenue is 95 more than the total number of houses on Algebra Avenue. The number of two-story houses is three times greater than the number of three-story houses. How many houses are on Algebra Avenue?

The number of houses on Algebra Avenue are 76 houses

Step-by-step explanation:

The given information are;

Buildings on Algebra Avenue in Mathpolis = 2 or 3 stories high

Total number of stories = 95 + Total number of houses

The number of two-story houses = 3× The number of three-story houses

Let the number of three-story houses = X

Therefore, the number of two-story houses = 3 × X

Total number of stories = 3×X + 2×3×X = 9·X

The total number of houses = X + 3 × X = 4·X

Given that, the total number of stories = 95 + Total number of houses, we have;

9·X = 95 + 4·X

9·X - 4·X = 95

5·X = 95

X = 95/5 = 19

X = 19

The total number of houses = 4·X

Therefore, the total number of houses = 4 × 19 = 76 Houses.

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