Question

2. A 4-oz. steak contains 700 mg of potassium. It is recommended for the average person to consume at least 3,500mg of potassium a day. If you ate a 10-oz. steak for dinner, what percent of your daily value of potassium did youeat?

Answer 1

We know that 4 oz of steak contains 700 mg of potassium. We want to know how many mg of potassium a 10 oz steak has. The bigger the steak the more potassium it has, so it is a directly proportional relationship. We can apply a rule of three to find the value we want as shown below:

`(4)/(10)\frac{\text{ oz}}{\text{ oz}}=(700)/(x)\frac{\text{ mg}}{\text{ mg}}`

Since hte relationship is proportional we don't need to invert any of the fractions. The first step is to cross multiply and then solve for x.

`\begin{gathered} 4\cdot x=10\cdot700 \\ 4\cdot x=7000 \\ x=(7000)/(4) \\ x=1750\text{ mg} \end{gathered}`

A 10 oz steak contains 1750 mg of potassium. We want to know how many percent of the daily value we consumed by eating that steak. To do that we can create another rule of three as shown below:

`(1750)/(3500)\frac{\text{ mg}}{\text{ mg}}=(x)/(100)\frac{\text{ \%}}{\text{ \%}}`
`\begin{gathered} 3500\cdot x=1750\cdot100 \\ 3500\cdot x=175000 \\ x=(175000)/(3500) \\ x=50\text{ \%} \end{gathered}`

We ate 50 % of the daily value of potassium recommended.