Question

Gina's art teacher mixes 9 pints of yellow paint with 6 pints of blue paint create green paint. Gina mixes 4 pints of yellow paint with 3 pints of blue paint. Did Gina use the same ratio of yellow to blue paint instructed by her teacher? Explain.

My Answer:
9/6=1 and 3/6= 1 and 1/2 or 1.5
4/3=1 and 1/3 or 1.3333
Then I compared the fractions and found if I am not mistaken that 1 and 1/3 is less than 1 and 1 and 1/2 but I am having trouble explaining why Gina did not use the same ratio.

Can you please help me and check and see if I got my answer correct.

Ty

Answer 1

when comparing ratios, it is often a good idea to have the parts represented by the same number.

teacher:
yellow : blue = <b>9 : 6</b>

Gina:
yellow : blue = 4 : 3 = <b>8 : 6</b>

So, what do you think?

Answer 2

I tried that too and got the same answer 9/6 and 8/6 so I know that Gina did not use the same ratio of yellow paint to blue paint as instructed by her teacher because the teacher used 1/6 more paint than Gina.

Would my above answer be correct?

Answer 3

yes

I boils down to simply showing that
9:6 ≠ 4:3

Answer 4

Thank you for making me think and pointing me in the right direction as well. I would like to ask one more question though. How do you know in a word problem with a ratio whether to divide or multiply?

Answer 5

teacher: 9:6 and Gina: 4:3
If you multiply 4 and 3 by 9 and 9 and 6 by 4 you get
teacher: 36:24
Gina: 36:27
so no they do not have the same RATIO.

Answer 6

The answer is No, Gina art teacher used the ratio 9:6 or simplified 3:2. Gina used ratio 4:3.

Answer 7

ratio