Question

aylor and Natsumi are making block towers out of large and small blocks. They are stacking the blocks on top of each other in a single column. Taylor uses 4 large blocks and 2 small blocks to make a tower 63.8 inches tall. Natsumi uses 9 large blocks and 4 small blocks to make a tower 139.8 inches tall. How tall is each large block and each small block

Answer 1

The height of a large block is of 12.1 inches and of a small block is of 7.7 inches.

Explanation:

This question is solved using a system of equations.

I am going to say that:

x i the height of a large block.

y is the height of a small block.

Taylor uses 4 large blocks and 2 small blocks to make a tower 63.8 inches tall.

This means that:

`4x + 2y = 63.8`

Simplifying by 2:

`2x + y = 31.9`

So

`y = 31.9 - 2x`

Natsumi uses 9 large blocks and 4 small blocks to make a tower 139.8 inches tall.

This means that:

`9x + 4y = 139.8`

Since
`y = 31.9 - 2x`

`9x + 4(31.9 - 2x) = 139.8`

`9x + 127.6 - 8x = 139.8`

`x = 12.1`

`y = 31.9 - 2x = 31.9 - 2(12.1) = 7.7`

The height of a large block is of 12.1 inches and of a small block is of 7.7 inches.