Answer:
2 / 15 of the recommended amount
Explanation:
We know that 3/4 of a cup contains 1 /10 of the recommended amount. Therefore, the ratio of cups to recommended amount is
cups : recommended amount = 3 /4 : 1/10 < ---- (a)
Now, how much of the recommended amount does 1 cup of oatmeal contain?
Let us call this unknown value ( the recommended amount in 1 cup) x, then the ratio
cups: recommended amount is
cups : recommended amount = 1 : x <----- (b)
The ratio (a) and (b) must be equal; therefore,
[tex]\frac{3/4}{1/10}=\frac{1}{x}[/tex]Now cross multiplication gives
[tex](3/4)x=(1)(1/10)[/tex][tex]\Rightarrow\frac{3x}{4}=\frac{1}{10}[/tex]Cross multiplying one more time gives
[tex](3x)(10)=(4)(1)[/tex][tex]30x=4[/tex]finally, dividing both sides by 30 gives
[tex]\frac{30x}{30}=\frac{4}{30}[/tex][tex]x=\frac{4}{30}[/tex][tex]x=\frac{4\div2}{30\div2}=\frac{2}{15}[/tex][tex]\boxed{x=\frac{2}{15}\text{.}}[/tex]Therefore, there is 2/ 15 of the recommended amount in 1 cup of oatmeal.