Answers to the Pyramid Fraction Exercise

 The problem is to build a Pyramid using small blocks of tan and white starting with a base of 9 x 9 blocks and building up from there.  There must be a ratio of 1 out of 5 blocks in the Pyramid being tan, and the remaining white.

The problem also states that the blocks will be manufactured using a batch method.  The "Mixed" batch will make 3 tan blocks and 1 white one.

The other batch will make all white blocks.

The question is then how many "Mixed" batches will be required to make enough Tan blocks?...and correspondingly, how many regular batches will be required to make up the remaining white blocks?

The first step is to calculate the total number of blocks required.  The problem almost gave us the answer:

Adding up each layer, the total is 140 blocks.

The second step is to calculate the total number of tan blocks required.  Since the ratio is 1 tan block for every 5 blocks, the total number of tan blocks required is 28.

Now the hard part...how many mixed batches are required?

The are 3 tan blocks per one mixed batch.  Divide this into the total number of tan blocks required to find the number of mixed batches. (we are trying to find the number of "groups of three" fit inside the number 28).

Since there are a little over 9 mixed batches required, we best make 10 batches...and eat the left over blocks...unless you painted them, then never mind.

Now to find the white ones:  We know there are 140 total blocks, and 28 of those are tan.  hence, the total number of white blocks are 

140 - 28 = 112 white blocks

We previously made 10 "mixed" batches which each had 1 white block.  No fraction division required here, we know we have 10 white ones from the mixed batches.

112 - 10 = 102 white blocks remaining

We repeat the division process with the regular batches using the ratio of 4 white blocks per batch:

We need 25 1/2 regular batches, so we might as well make 26 and find a use for the left overs.