Question

Jerome takes a math course and a science course for summer school. For every 5 hours Jerome spends studying math, he studies science for 4 hours. If Jerome spent a total of 54 hours studying last week, then how long did he study math?

Answer 1

Answer:

$y= \frac{54*4}{9}=24$

And then we can solve for x like this:

$x = \frac{5*24}{4}=30$

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:

$x+ y = 54$   (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:

$\frac{x}{y}=\frac{5}{4}$

And we can solve for x like this:

$x = \frac{5y}{4}$

And we can replace this into equation (1) and we got:

$\frac{5y}{4} + y = 54$

And if we do the algebra we got:

$\frac{9y}{4} =54$

$y= \frac{54*4}{9}=24$

And then we can solve for x like this:

$x = \frac{5*24}{4}=30$

And the final solution would be 30 hours for math and 24 for the science course.

Answer 2

Answer:

Jerome spent $30$ 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

$5:4$ respectively.

The total ratio is $5+4=9$.

If Jerome spent a total of $54$ hours studying last week, then the number of hours he spent studying mathematics is

$=\frac{5}{9}\times 54$.

$=\frac{5}{1}\times 6$.

$=30$ hours.