Certainly! Let's break down the problem step by step.
First, let [tex]\( x \)[/tex] represent the time Cora spends revising for French in hours.
Given the ratio of the time spent on History to French is [tex]\( 7:2 \)[/tex], the time she spends on History can be expressed in terms of [tex]\( x \)[/tex]:
[tex]\[ \text{Time spent on History} = \frac{7}{2}x \][/tex]
We also know that the time spent on History is 20 hours more than the time spent on French:
[tex]\[ \frac{7}{2}x = x + 20 \][/tex]
To solve for [tex]\( x \)[/tex], we can set up the equation:
[tex]\[ \frac{7}{2}x = x + 20 \][/tex]
Next, we need to clear the fraction by multiplying every term by 2:
[tex]\[ 7x = 2x + 40 \][/tex]
Now, we isolate [tex]\( x \)[/tex] by subtracting [tex]\( 2x \)[/tex] from both sides of the equation:
[tex]\[ 5x = 40 \][/tex]
Then, we solve for [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[ x = \frac{40}{5} \][/tex]
[tex]\[ x = 8 \][/tex]
So, Cora spends 8 hours revising for French.
Now, we find the time Cora spends revising for History:
[tex]\[ \text{Time spent on History} = x + 20 = 8 + 20 = 28 \text{ hours} \][/tex]
Finally, we calculate the total time Cora spends revising for both subjects:
[tex]\[ \text{Total time} = \text{Time spent on French} + \text{Time spent on History} \][/tex]
[tex]\[ \text{Total time} = 8 + 28 = 36 \text{ hours} \][/tex]
Therefore, the total time Cora spends revising is 36 hours.
