Three different shades of paint are created using only red and yellow paint. The different mixtures are shown below. Marmalade, red is equal to three-eighths. Sunburst, red to yellow is equal to 13 to 27. Tangerine, red is equal to 36 percent. Which shade of paint uses the lowest proportion of red paint? You must show your working.
So what we’re looking to do in this question is find the lowest proportion of red paint in our mixture for one of our colors. Okay, so great. How are we going to do that? And what does the proportion mean? Well, it means the lowest proportion of red compared to the proportion of yellow. So the way that we’re going to do that is we’re gonna have to compare the red proportion for each of our paints. And we’re gonna do that by making them all the same, so either a fraction, decimal, or percentage. What I’m gonna do is I’m gonna change them all to a decimal, because that’s gonna be the easiest to compare.
What if we start off with marmalade? We’re told that the red is three-eighths of the paint. So then, we’d know that five-eighths of the paint are going to be yellow. Well, three-eighths means three divided by eight. So we could just type this into our calculator. And we get 0.375. However, if we want to do it using a written method, we could use short division. See how many eights are going to three, which is zero. So then we put zero, have a decimal point. And we carried the three. And when we do, how many eights are in 30? Well, it’s three remainder six because we have 24 is three multiplied by eight. And then we need another six to get to 30. So then we carry the six. When we do, how many eights are into 60? Well, it’s seven because eight sevens are 56 remainder four. Then, how many eights are into 40? And we get five. So we get our 0.375. Okay, great. So we’ve now converted that to a decimal. Let’s move on to sunburst.
Well, for sunburst, we’re told the ratio of red to yellow is 13 to 27. The first thing to note is that ratios are always written in the correct order. So if we’ve written red to yellow, then the numbers are red to yellow. So that means the 13 parts refers to red. So therefore, we can think of red as being 13 parts out of a total of 13 plus 27 parts because it’s 13 out of all of the parts. Well, 13 plus 27 is 40. And we can have that because 13 add seven is 20 add 20 is 40. So we can write this as 13 over 40 because 13 out of 40 can be written as a fraction. And again, we can calculate this. And when we calculate this, we get 0.325. Okay, great. So now, finally, we move on to tangerine.
Well, for tangerine, we’re told that the red is equal to 36 percent. Well, 36 percent means 36 out of 100. So therefore, we can rewrite 36 percent as 36 over 100. Now, if we divide 36 by 100, again we can calculate it. Or we could use a mental method because if you divide by 100, it means that each of the digits in 36 moves two place values to the right. So three goes from being a ten to a tenth. So therefore, as a decimal, the proportion of red in tangerine is 0.36.
So now what we can do is we can compare our decimals. So none of them have any units. Then they all have three tenths. So this doesn’t help us split it. So we’re gonna have to look at the hundredths column. So we can see that two is the lowest number of hundredths. So therefore, 0.325 is going to be the lowest value of our decimals. Then, the second lowest is gonna be 0.36 because six is the next value of hundredths, because it’s less than seven, but greater than two. So we can say that 0.36 is greater than 0.325. And therefore, finally, the greatest decimal is 0.375. And I’ve written it all here using inequality signs because we can say that 0.36 is greater than 0.325, but less than 0.375.
So now we need to answer the question. Well, the question asks which shade of paint uses the lowest proportion of red paint. So therefore, we can say that sunburst is the paint that uses the least proportion of red paint. And that’s because 0.325 or 13 out of 40 is the amount of red paint used in the sunburst paint.