PAINT PROBLEM
Yellow and red paint are mixed at a paint factory to make two orangy colours. The
“Raro” colour is made from mixing the 1 part yellow to 1 part red. The “Tango” is made
from mixing 1 part yellow to two parts red.
“Raro” is sold in 2 litre tins and “Tango” in 3 litre tins.
Answer these.
1) Which of the two mixes is more orange? Why?
2) What is the ratio of yellow to red in “Raro”?
3) What fraction is yellow in “Raro”?
4) What is the ratio of yellow to red in “Tango”?
5) What fraction is yellow in “Tango”?
Buddy buys a tin of each colour and mixes them both together to make 5 litres of
what he calls “Sunset”.
6) Is the new colour more or less orange than “Raro”? Explain your answer
He says the “Raro” is 1/2 yellow and the “Tango” is 1/3 yellow so adding these gives
“Sunset” a proportion of 2/5ths yellow. He says this is not how to add fractions!
7) Is Buddy correct? Is there another answer?
8) What is the ratio of yellow to red in “Sunset”?
Exactly halfway between the colour “Raro” (1:1) and “Tango” (1:2) is another colour
called “Mandarin”.
9) What is the ratio of yellow to red in “Mandarin”?
10) What is the proportion of yellow in “Mandarin”?
11) Explain how to mix 2L tins of “Raro” and 3L tins of “Tango” to make “Mandarin”
PROBLEM 2
Yellow and red paint are mixed at paint factory to make two orangy colours. The
“Raro” colour is made from mixing the 1 part yellow to 1 part red. The “Tango” is made
from mixing 1 part yellow to two parts red. “Raro” is sold in 2 litre tins and “Tango” in 2 litre tins.
(Note that the tins are the same size.)
Answer these.
1) Which of the two mixes is more orange? Why?
2) What is the ratio of yellow to red in “Raro”?
3) What proportion is yellow in “Raro”?
4) What is the ratio of yellow to red in “Tangello”?
5) What proportion is yellow in “Tangello”?
Buddy buys a tin of each colour and mixes them both together to make 4 litres of
what he calls “Bluemoon”.
6) Is the new colour more or less orange than “Raro”?
He says the “Raro” is 1/2 yellow and the “Tangello” is 1/3 yellow so adding like we add
fractions gives “Bluemoon” a proportion of 5/6ths yellow. He says this is how to add
fractions but there is not that much yellow in “Bluemoon”. Something is wrong!
7) Is Buddy correct? Is there a better answer?
8) What is the ratio of yellow to red in “Bluemoon”?
Exactly halfway between the colour “Raro” (1:1) and “Tangello” (1:2) is another colour
called “Mandarine” which Buddy says has ratio of 1:1.5 or 2:3 yellow to red.
9) Is halfway between 1:1 and 1:2 exactly 2:3? Is Buddy correct?
10) What is the proportion of yellow in “Mandarine”?
11) Explain how to mix 2l tins of “Raro” and “Tangello” to make “Mandarine”
PAINT PROBLEM ANSWERS
1) More Orange? What does this mean? Raro is in the middle so could be a ‘truer’ orange.
Tango will be a deeper orange with more red in it.
2) 1:1
3) ½
4) 1:2
5) 1/3
6) Again what does this question mean? One way to explain this is to say it has more red than
Raro (so would appear darker (more reddy) than Raro) and less red than Tango (so would
appear lighter (or more yellowy) than Tango).
7) Buddy is correct. Model this with unifix or multilink blocks, and put both lots into a
container. There is no other answer.
8) 2:3
9) Your answer to this problem should be discussed with your teacher
10) 5/12ths from the ratio 5:7 This answer comes from the discussion for question 9
11) Mixing the Mandarin is tricky with one 2L tin and one 3L tin but with multiple tins of each
it can be done! Three tins of Raro gives 3:3 and 2 tins of Tango gives 2:4. Adding this gives
us 10 litres of Mandarin mixed perfectly 5:7.
Problem 2
1) More Orange? What does this mean? Raro is half and half so could be more “orange like”.
Tangello will be a deeper reddy orange.
2) 1:1
3) 1/2
4) 1:2
5) 1/3
6) Bluemoon orange is between Raro orange and Tangello orange but more yellow than
Sunset.
7) Buddy is astute to notice he is “wrong”! He added ½ (from one yellow out of two for raro)
and 1/3 (from one yellow out of three for tangello), which is 3/6 + 2/6 = 5/6. The same
logic says that to work out the amount of red, 1/2 + 2/3 = 3/6 + 4/6 = 7/6, which is more
than in the whole paint tin! Actually, it is the amount of red in two paint tins.
If we put these together, they will give us the correct ratio of yellow to red, 5:7.
8) 5:7
9) Discuss your answer to this problem with your teacher
10) 5/12ths from the ratio 5:7
11) Mixing the Mandarine is very tricky with these 2L tins, but it can be done! 3 tins of 1:1 and
3 tins of 1:2 will give the correct mixture. This in effect creates the same size (Litre) units
and so preserves all the relationships.
