Question

It is recommended that adults consume at least 1,000 mg of calcium every day. One ounce of whole milk contains about 25 mg of calcium, and one ounce of cheddar cheese contains 200 mg of calcium. If a person meets the recommendation by consuming x ounces of whole milk and y ounces of cheddar cheese, then 25x + 200y ≥ 1,000.Give three different amounts of milk and cheese that a person could consume to meet the recommendation.

Answer 1

20 ounces of milk and 3 ounces of cheddar cheese

30 ounces of milk and 4 ounces of cheddar cheese

40 ounces of milk and 5 ounces of cheddar cheese

Explanation:

Consider the inequality
`25x+200y\geq 1000`

Here, x denotes ounces of whole milk and y denotes ounces of cheddar cheese.

To write: three different amounts of milk and cheese that a person could consume to meet the recommendation

Solution:

Take
`x=20,y=3`

`25(20)+200(3)\geq 1000\\500+600\geq 1000\\1100\geq 1000`

So,
`x=20,y=3` satisfy the inequality
`25x+200y\geq 1000`

Take
`x=30,y=4`

`25(30)+200(4)\geq 1000\\750+800\geq 1000\\1550\geq 1000`

So,
`x=30,y=4` satisfy the inequality
`25x+200y\geq 1000`

Take
`x=40,y=5`

`25(40)+200(5)\geq 1000\\1000+1000\geq 1000\\2000\geq 1000`

So,
`x=40,y=5` satisfy the inequality
`25x+200y\geq 1000`

Therefore,

three different amounts of milk and cheese that a person could consume to meet the recommendation are as follows:

20 ounces of milk and 3 ounces of cheddar cheese

30 ounces of milk and 4 ounces of cheddar cheese

40 ounces of milk and 5 ounces of cheddar cheese