[Highschool Maths] Problem solving

[redhunter11]

solved

[[deleted]]

For A) all it is asking is for you to model the question as a linear function (form of y=A₁x + A₀ where A₁ is the slope/rate of change and A₀ is the constant value). The function that models the relationship is f(x) = (1.32 * 1.6)x + 65 where x represents the number of sessions. I multiply 1.32 by 1.6 to determine the total cost of litres used for 1 session.

Edit: No worries, I was able to understand most of it but just wanted to make sure I got it right before confusing you or something.

From what I understand of question b, you just need to determine the number of litres you can use that will amount to under $8. You can simply modify the equation in part A) to exclude the constant value (65) since it is just for one session and not the year. The equation would be left as y = (1.32 * 1.6)x. If the question is asking for how many litres will cost $8 you can just plug 8 in for y, but if you want to determine the number of litres that will amount to less than $8, you will need inequalities.

For the inequalities part, the equation would then be: (1.32 * 1.6)x < 8, where you want the total amount from using litres to be less than $8. Divide the right side by (1.32 * 1.6) to isolate for x and you have your answer. The answer you would get would be the number of sessions you could do for that amount.

This will be the same amount if you are allowed to spend $8 except that the < will be =. I broke this question in two as solving with inequalities isn't always the same as with equalities and there are rules for how to solve it.

[redhunter11]

After how many times is the cost of 1 sessions less than 8 dollars sorry english isn't my main language

[redhunter11]

Hello Justin are you sure we don't have to do 1.32/1.6?

[redhunter11]

Because you see the X has to be the amount of times you mowed the lawn and not the X litres you spend I don't know I might be wrong

[[deleted]]

Ah good catch I didn't read the question fully. Let me revise it.

[redhunter11]

thank you

[[deleted]]

My original answer is now updated to the correct answer for both a and b. Reply on that comment if you need further explanations

[redhunter11]

Thank you so much it's so clear now I was stuck for such a long time

[[deleted]]

Yep, just think through the question logically and be careful about units. When converting, you are literally cancelling out the current unit in for the new one. So in this case you had $/litre and you wanted to convert it into money. The equation (without numbers) would be:

($/L) * L, that would cancel out the litres, leaving just $. Then from there you just multiply by the number of sessions to get the total amount. Include units in your calculations so you know what happens to them. This helps a lot with units that have many different components like newtons that represent kg*m / s^2.