Question

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?

Answer 1

76

Explanation:

So I'm going add on to Mathmate to save time of explaining.

So he got 57 right? He forgot one point.

Let's suppose --> x = # of 2 story houses, y = # of 3 story houses

We already know from Mathmate that y = 19 from pushing the equation -->

2x + 3y - 95 = x + y and so on. . . --> we can from there, continue pushing this question starting with the fact that y = 19, 19(3) = 57 so already know that the amt. of y stories is 57 --> BUT 57 IS NOT OUR FINAL ANSWER. x = 57 since x = 3y as given in the question and so, 57 x 2 = 114 stories in the 2 story section. Add amts. of x and y respectively 57 and 19 and we get 76.

Check answer:

114 stories + 57 stories = 171 stories

amt. of stories is 95 greater than amt. of houses => 171 - 76 = 95

Thus, 76 is our FINAL answer

Hope this helps!

Answer 2

Explanation:

Let

b=number of two storey houses,

t=number of three storey houses,

the total number of stories on Algebra Avenue is 95 more than the total number of houses on Algebra Avenue.

2b+3t-95=b+t =>

b+2t=95 .................(1)

The number of two-story houses is three times greater than the number of three-story houses.

b=3t .....................(2)

Substitute (2) in (1)

3t+2t = 95

5t=95

t=19 ......................(3)

substitute (3) in (2)

b=3t=3*19 = 57 .........(4)

Substitute (3) & (4) in (1)

b+2t=57+2*19=95 checks

Substitute (3) & (4) in (2)

b=3t=3*19=57 checks.