1. Karol uses Gluze and Blurpos to make Zippies. His recipe uses 4 cups of Gluze and 3 cups of Blurpos to make 60 Zippies. He can also make larger batches of Zippies using these same ratios.
(a) On Monday, Karol uses 28 cups of Gluze when he makes Zippies. Determine the number of cups of Blurpos that he uses.
(b) On Tuesday, Karol uses 48 cups of one of the ingredients and $N$ cups of the other ingredient when he makes Zippies. Determine the two possible values of $N$.
(c) On Wednesday, Karol has 64 cups of Gluze and 42 cups of Blurpos available. Determine the largest number of Zippies that he can make.
(d) On Thursday, Karol makes Zippies to sell. His only costs come from purchasing Gluze and Blurpos. He sells each Zippie for $\$ 0.50$ and makes a profit of $\$ 0.30$ from each Zippie sold. Karol pays $\$ 1.80$ for each cup of Gluze. Determine how much Karol pays per cup of Blurpos.
1. (a) Since Karol uses 28 cups of Gluze, and the recipe calls for 4 cups of Gluze, he must have repeated the recipe $28 \div 4=7$ times.
Since the recipe calls for 3 cups of Blurpos, and the recipe was repeated 7 times, he must have used $7 \times 3=21$ cups of Blurpos.
(b) Suppose that Karol uses 48 cups of Gluze.
Since $48 \div 4=12$, he uses his recipe 12 times and so uses $12 \times 3=36$ cups of Blurpos. Suppose instead that Karol uses 48 cups of Blurpos.
Since $48 \div 3=16$, he uses his recipe 16 times and so uses $16 \times 4=64$ cups of Gluze.
Therefore, the two possible values of $N$ are 36 and 64 .
(c) Karol starts with 64 cups of Gluze and 42 cups of Blurpos. One of these ingredients will be the "limiting ingredient" ; that is, when Karol repeats his recipe, he will probably run out of one of the ingredients before the other.
If Karol used all 64 cups of Gluze, then he must have used his recipe $64 \div 4=16$ times. If Karol used all 42 cups of Blurpos, then he must have used his recipe $42 \div 3=14$ times. Therefore, he can make the recipe at most 14 times since after the 14 th time, he would run out of Blurpos.
Each time Karol uses his recipe, he makes 60 Zippies.
When he uses his recipe 14 times, he makes $14 \times 60=840$ Zippies.
(d) We start by assuming that Karol makes 1 recipe worth of Zippies.
In other words, suppose that Karol makes 60 Zippies using 4 cups of Gluze and 3 cups of Blurpos.
He sells each Zippie for $\$ 0.50$, which earns him $60 \times \$ 0.50=\$ 30.00$.
His profit on each Zippie is $\$ 0.30$, which means that his total profit is $60 \times \$ 0.30=\$ 18.00$. Since he earns $\$ 30.00$ and his profit is $\$ 18.00$, his costs must be $\$ 30.00-\$ 18.00=\$ 12.00$. Since Karol pays $\$ 1.80$ for each cup of Gluze, he pays a total of $4 \times \$ 1.80=\$ 7.20$ for Gluze.
This means that he pays $\$ 12.00-\$ 7.20=\$ 4.80$ for Blurpos.
Since he uses 3 cups of Blurpos, Karol pays $\$ 4.80 \div 3=\$ 1.60$ per cup of Blurpos.