Question

the blueprint dimensions of the playground are 23/147 yd x 3/14 yd after reducing them by the factor of 2/147 what are the original dimensions if the playground in yards

Answer 1

The original dimensions of the park are:

(23/2) yards by 7 yards.

Explanation:

Suppose that you have a given dimension X

if you want to reduce that dimension by a scale factor k, such that:

0 < k < 1

The reduced dimension is just:

X' = k*X

Now let's solve the problem:

We know that the dimensions on the blueprint are:

(23/147)yd by (3/14)yd

And the original dimensions are:

A yd by B yd

We know that, to get the blueprint dimensions, we reduced the original dimensions by a factor of 2/147

Then we just have that:

(2/147)*A = 23/147

(2/147)*B = 3/14

Now we just can solve these two equations for A and B

A = (23/147)*(147/2) = 23/2

B = (3/14)*(2/147) = (3/7)*(1/147) = 49/7 = 7

Then the original dimensions of the park are:

(23/2) yards by 7 yards.