Answer:
Jerome spent [tex]30[/tex] hours studying mathematics
Step-by-step explanation:
We were given that every 5 hours Jerome spends studying math. he studies science for 4 hours.
The ratio of Mathematics to Science is
[tex]5:4[/tex] respectively.
The total ratio is [tex]5+4=9[/tex].
If Jerome spent a total of [tex]54[/tex] hours studying last week, then the number of hours he spent studying mathematics is
[tex]=\frac{5}{9}\times 54[/tex].
[tex]=\frac{5}{1}\times 6[/tex].
[tex]=30[/tex] hours.
Answer:
[tex] y= \frac{54*4}{9}=24[/tex]
And then we can solve for x like this:
[tex] x = \frac{5*24}{4}=30[/tex]
And the final solution would be 30 hours for math and 24 for the science course.
Step-by-step explanation:
We need to define some notation first. Let
x= number of hours that he spent for the math course
y = number of hours that he spent for th science course
We have that the total of hours is 54, and we can write that like this:
[tex] x+ y = 54[/tex] (1)
And the other conditions is: " For every 5 hours Jerome spends studying math, he studies science for 4 hours" And we can write this like that:
[tex] \frac{x}{y}=\frac{5}{4}[/tex]
And we can solve for x like this:
[tex] x = \frac{5y}{4}[/tex]
And we can replace this into equation (1) and we got:
[tex] \frac{5y}{4} + y = 54[/tex]
And if we do the algebra we got:
[tex] \frac{9y}{4} =54[/tex]
[tex] y= \frac{54*4}{9}=24[/tex]
And then we can solve for x like this:
[tex] x = \frac{5*24}{4}=30[/tex]
And the final solution would be 30 hours for math and 24 for the science course.
