Karl has two bags of marbles. Bag A has 40 percent green marbles, and bag B has 60 percent green marbles. Combined, the two bags contain a total of 15 green marbles. Which equation models this relationship, where 𝑎 is the number of marbles in bag A and 𝑏 is the number of marbles in bag B? Is it option A) 15 is equal to 0.6𝑎 plus 0.4𝑏, option B) 15 is equal to 60𝑎 plus 40𝑏, option C) 15 is equal to 40𝑎 plus 60𝑏, or option D) 15 is equal to 0.4𝑎 plus 0.6𝑏?
We are told in the question that, combined, the two bags contain 15 green marbles. All four options have 15 on the left-hand side. Bag A has 40 percent green marbles. The word percent means out of 100. Therefore, 40 percent is the same as 40 out of or over 100. As the line in the fraction means divide, we can divide 40 by 100. Dividing any number by 100 moves all the digits two places to the right. Therefore, 40 divided by 100 is equal to 0.4. As there were a total of 𝑎 marbles in bag A, the number that are green is 0.4 multiplied by 𝑎.
We can repeat this process for bag B, which had 60 percent green marbles. 60 percent is equivalent to the fraction 60 out of 100 and the decimal 0.6. As there are a total of 𝑏 marbles in bag B, the number that are green is 0.6 multiplied by 𝑏. This means that the total number of green marbles is 0.4𝑎 plus 0.6𝑏. The correct answer is option D, 15 is equal to 0.4𝑎 plus 0.6𝑏.
Note that option A has 𝑎 and 𝑏 the wrong way round. This is 60 percent from bag A and 40 percent from bag B. Options B and C have not converted the percentages into decimals, which means that these are incorrect answers. The equation that models the relationship is 15 equal 0.4𝑎 plus 0.6𝑏.