Albert has a home screen printing business. He has designed a bracelet and T‑shirt for St. Patrick’s Day which both use a special ink, available for a limited time from his supplier. Albert has already begun taking and fulfilling orders for merchandise. Albert noticed that 457.5 ml of the special ink was used to make 25 bracelets and 8 T-shirts, and he used another 712.5 ml of ink to make 14 bracelets and 18 T-shirts.
Albert hopes he’ll have enough ink to fulfill an order for 42 bracelets and 21 T‑shirts since his printer indicates that he has 1 L of the special ink remaining. If Albert will have enough ink, how many milliliters of ink will be left after fulfilling the order? If, on the other hand, Albert does not have a sufficient amount of ink to fulfill the order, by how many milliliters is he short? Express your answer as a decimal to the nearest hundredth.
what is the rule if the input is 2 and the output is 5?
To solve this problem, let's first calculate the total amount of ink used to make the bracelets and T-shirts in the previous orders. From the given information, we know that:
457.5 ml of ink was used to make 25 bracelets and 8 T-shirts.
712.5 ml of ink was used to make 14 bracelets and 18 T-shirts.
Let's calculate the amount of ink used per bracelet in the first and second order:
1. In the first order, the amount of ink used per bracelet is 457.5 ml / 25 bracelets = 18.3 ml/bracelet.
2. In the second order, the amount of ink used per bracelet is 712.5 ml / 14 bracelets ≈ 50.89 ml/bracelet.
Now let's calculate the amount of ink used per T-shirt in the first and second order:
1. In the first order, the amount of ink used per T-shirt is 457.5 ml / 8 T-shirts = 57.19 ml/T-shirt.
2. In the second order, the amount of ink used per T-shirt is 712.5 ml / 18 T-shirts ≈ 39.58 ml/T-shirt.
To determine if Albert has enough ink to fulfill the order of 42 bracelets and 21 T-shirts, we can calculate the total amount of ink required:
Total ink required = (Amount of ink per bracelet * Number of bracelets) + (Amount of ink per T-shirt * Number of T-shirts)
Total ink required = (18.3 ml/bracelet * 42 bracelets) + (39.58 ml/T-shirt * 21 T-shirts)
Total ink required = 769.8 ml + 830.18 ml
Total ink required = 1599.98 ml
Since Albert has 1 L of ink remaining, which is equal to 1000 ml, we can now calculate the difference between the total ink required and the ink he has remaining:
Difference = Total ink required - Ink remaining
Difference = 1599.98 ml - 1000 ml
Difference = 599.98 ml
Therefore, if Albert has enough ink, he will have 599.98 ml of ink left after fulfilling the order.