Ch 4 Ratios

Question 1

Ratios fact 1

Answer 1

Ratios are powerful on D/S. They often provide enough info to ans the question. If 2 quantities have a constant ratio, they are in direct proportion to each other.

Question 2

Ratio fact 2

Answer 2

To save time on proportions, always cancel before cross multiplying but you can only cancel either vertically or horizontally across an equal sign.

NEVER cancel factors diagonally across an equal sign. Always cross multiply.

Question 3

If the scale model of cube sculpture is .5cm per every 1 m of the real sculpture, what is the volume of the model , if the volume of the real sculpture is 64m³?

Answer 3

Real V= s³= 64= s³= s=4 (The length of a side on the real sculpture is 4m)

Model/Real: .5 cm/1m = xcm/4m ( Set up proportion and solve for x, the side of the model) .5/1=x/4 x=2 cm ( The length of a side on the model is 2 cm) Model: V= s³ = (2)³ = 8. (The volume of the model is 8 cm³).

** Key to this question is first figuring out the length of one side) and than find the volume.

Question 4

Alexandra needs to mix cleaning solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Alexandra makes a mistake and mixes in half as much bleach as she ought to have. The total solution consists of 27 ml. How much bleach did Alexandra put into the solution?

Answer 4

** The key to this question is to recognize that the new mix of bleach is half as much which is half than the original bleach mix. Half as much is same as half of. Double would be twice of.

Original Mix Ratio: B/W: 1x/4x

Revised Mix Ratio: B/W: .5x/4x ⇒ .5 is half as much Bleach

.5x+4x=27

4.5x=27

45x/10=27 ⇒ x= 27* 10/45 ⇒x = 3*10/5 = 3*2 = 6

.5x= .5(6)= 3 bleach