Cora is building towers of two different sizes using prism- and pyramid-shaped blocks. The diagram shows the ratio of prisms and

Question

3 years ago

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Cora is building towers of two different sizes using prism- and pyramid-shaped blocks. The diagram shows the ratio of prisms and

pyramids in each tower. A tape diagram with 2 tapes of unequal lengths. The first tape has 4 equal parts. A curved bracket above the first tape is labeled Prisms. The second tape has 1 part of the same size as in the first tape. A curved bracket below the second tape is labeled Pyramids. A tape diagram with 2 tapes of unequal lengths. The first tape has 4 equal parts. A curved bracket above the first tape is labeled Prisms. The second tape has 1 part of the same size as in the first tape. A curved bracket below the second tape is labeled Pyramids. The table shows the number of prisms and the number of total blocks that Cora will use on each of her towers. Based on the ratio, complete the missing values in the table. Tower Prisms Total blocks AAA 161616 BBB 353535

Mathematics

2 answers:

Musya8 [376] · Answer 1 · 2022-12-13T02:27:13+03:00

There are 20 blocks needed for tower A, and 43.75 blocks needed for tower B

From the tape diagrams, we have the following ratio

Prism : Pyramid = 4 : 1

From the table, we have:

Tower A = 16 prisms

So, the ratio becomes

16 : Pyramid = 4 : 1

Multiply the ratio on the right-side by 4

16 : Pyramid = 16 : 4

By comparison, we have:

Pyramid = 4

This means that, 4 pyramid blocks are needed for tower A

So, the total number of blocks needed is:

Total = Pyramid + Prism

This gives

Total = 4 + 16

Evaluate the sum

Total = 20

Hence, there are 20 blocks needed for tower A

For table B, we have:

Tower A = 35 prisms

So, the ratio becomes

35 : Pyramid = 4 : 1

Express as fractions

$\frac{Pyramid}{35} = \frac 14$

Multiply through by 35

Pyramid = 8.75

This means that, 8.75 pyramid blocks are needed for tower B

So, the total number of blocks needed is:

Total = 8.75 + 35

Evaluate the sum

Total = 43.75

Hence, there are 43.75 blocks needed for tower B