Question

Please help with this word problem, this is 6th grade mathematics.

Answer 1

2 / 15 of the recommended amount

Step-by-step 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,

`(3/4)/(1/10)=(1)/(x)`

Now cross multiplication gives

`(3/4)x=(1)(1/10)`
`\Rightarrow(3x)/(4)=(1)/(10)`

Cross multiplying one more time gives

`(3x)(10)=(4)(1)`
`30x=4`

finally, dividing both sides by 30 gives

`(30x)/(30)=(4)/(30)`
`x=(4)/(30)`
`x=(4/2)/(30/2)=(2)/(15)`
`\boxed{x=(2)/(15)\text{.}}`

Therefore, there is 2/ 15 of the recommended amount in 1 cup of oatmeal.