For an event that needs 750 cards in a blue-to-green ratio of 3 to 2, order 450 blue cards and 300 green cards. The ratio gives the relative sizes of the two groups. The total tells you how many cards go in each group.
Picture the order as five equal stacks. Three stacks are blue and two are green. Once you know how many cards make up one stack, you can find how many cards of each color to order.
Turn a part-to-part ratio into shares
A ratio of \(3:2\) compares the number of blue cards with the number of green cards. Add the two counts to find the number of equal parts in the order. Three of the five parts are blue, so blue cards make up \(\frac{3}{5}=60\%\) of the order. Green cards make up \(\frac{2}{5}=40\%\).
Divide 750 by five to get 150 cards per part. Multiply by three to get 450 blue cards. Two parts give 300 green cards. The counts add back to 750, and \(450:300\) reduces to \(3:2\) when you divide both numbers by 150.
Changing the order size changes the parts
For a 500-card order, one part is 100 cards. Order 300 blue cards and 200 green cards. The proportions stay the same as each stack gets smaller.
You can also start with the count for one color. If you already have 180 green cards, they represent two parts, so each part is 90 cards. Three parts call for 270 blue cards. The combined count is 450 cards.
Check what the second number refers to
Three blue cards for every two green cards means there are \(\frac{3}{2}=1.5\) times as many blue cards as green cards. The green cards are the reference quantity. There are 50% more blue cards than green cards.
When you say blue cards make up 60% of the order, the reference quantity is the total number of cards. The blue-to-total ratio is \(3:5\). The two percentages describe the same order using different denominators. When working with percentages, name the reference quantity before you calculate.
Keep the colors in the stated order. A green-to-blue ratio of 3 to 2 would allocate three of the five parts to green cards. Label each quantity so you can see which color the first number describes.
