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fomenos
3 years ago
10

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
Mathematics
1 answer:
frozen [14]3 years ago
7 0

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:

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.

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<h2>Answer:</h2>

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In the question,

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Therefore, on checking, we observe that,

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On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

<u>At, </u>

<u>n = 1</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0

which is true.

<u>At, </u>

<u>n = 2</u>

a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1

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<u>At, </u>

<u>n = 3</u>

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<u>At, </u>

<u>n = 4</u>

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<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

a_{n}=a_{n-1}+(n-1)^{2}

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