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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 :

Answer:

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

Step-by-step 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:

[tex]4x + 2y = 63.8[/tex]

Simplifying by 2:

[tex]2x + y = 31.9[/tex]

So

[tex]y = 31.9 - 2x[/tex]

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

This means that:

[tex]9x + 4y = 139.8[/tex]

Since [tex]y = 31.9 - 2x[/tex]

[tex]9x + 4(31.9 - 2x) = 139.8[/tex]

[tex]9x + 127.6 - 8x = 139.8[/tex]

[tex]x = 12.1[/tex]

[tex]y = 31.9 - 2x = 31.9 - 2(12.1) = 7.7[/tex]

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

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