Question

The ratio of solid beads to clear beads in a vase is 820. Select all the correct statements that tell if the operations will give an equivalent ratio.

A) Add 2 solid and 2 clear beads.


B) Subtract 8 solid and 6 clear beads.


C) Multiply the number of solid and clear beads by 2.


D) Divide the number of solid and clear beads by 4.


E) Multiply the number of solid and clear beads by 18.

Answer 1

C, D and E

Explanation:

Given

Represent solid beads with S and clear beads with C

So:

`S:C = 8:20`

Required

Select operations that give an equivalent ratio

First, we need to get the unit ratio

`S:C = 8:20`

Divide through by 4

`S:C = 2:5` -- This means that, after any operation. The equivalent ratio must be 2: 5

Option A: Add 2 to S and 2 to C

`S:C = 8:20`

Perform the operation

`S:C = 8 + 2 : 20 + 2`

`S:C = 10 : 22`

Divide through by 2

`S:C = 5:11`

Option B: Subtract 8 from S and 6 from C

`S:C = 8:20`

Perform the operation

`S:C = 8 - 8 : 20 - 6`

`S:C = 0 : 14`

Option C: Multiply S and C by 2

`S:C = 8:20`

Perform the operation

`S:C = 8*2:20*2`

`S:C = 16:40`

Divide through by 8

`S:C = 2:5`

Option D: Divide S and C by 4

`S:C = 8:20`

Perform the operation

`S:C = 8/2:20/4`

`S:C = 2:5`

Option E: Multiply S and C by 18

`S:C = 8:20`

Perform the operation

`S:C = 8*18:20*18`

`S:C = 144:360`

Divide through by 72

`S:C = 144/72:360/72`

`S:C = 2:5`

From the calculations above, options C, D and E gave an equivalent of 2:5.