Question

I just need the answers for this.im really confused

Answer 1

Question a)

We have weekly saving of $2.50, the target amount of $85.98 and the amount carried forward from birthday present of $35, We want to work out the number of weeks we need to save to buy season pass

By working backwards, the steps are
$85.98-35=50.98$ ⇒ We subtract the birthday money from the season-pass fee
$50.98/2.50 = 20.392$ ≈ 21 Weeks ⇒ We divide by the amount we save every week

The answer is rounded up to 21 weeks

Question b)

Let the number of weeks be '$x$' and the season-pass fee be '$y$'

The equation that represents the context is
$y=35+25x$ 

In words: To achieve the value $y$ we need to multiply $x$ by $2.50 (saving) and add $35 (birthday money) 

We know that $y=85.98$ as this is the amount we aim to achieve by saving $2.50 per week. Substituting this into the equation we formed earlier we have

$85.98=35+2.5x$ ⇒ Subtract 35 from both sides
$85.98-35=35-35+2.5x$
$50.98=2.5x$ ⇒ Divide both sides by 2.5
$\frac{50.98}{2.5}= \frac{2.5x}{2.5}$
$x=20.392$ ≈ 21

We round the answer to 21 weeks. We achieve the same answer with part a)

Question c)

This time, we aim to save $85.98 by the end of 11th week. We might need to adjust the amount we save per week. We will use the same equation we form in part b) but this time we will use the variable $'s'$ to represent the amount of weekly saving.

$y=35+11s$ ⇒ where $y$ is the season pass fee, '35' is the birthday money, '11' is the number of weeks, and $'s'$ is the amount of saving

We have $y=85.98$

$85.98=35+11s$
$85.98-35=11s$
$50.98=11s$
$s= \frac{50.98}{11}=4.6345$ ≈ 5

The answer is $5 to be saved for 11 weeks to achieve $85.98
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Use the same equation to work out the number of weeks we need to save $2.50 per week if we have to pay the higher price of season pass fee of $120.98

$y=35+2.50x$
$120.98=35+2.5x$
$120.98-35=2.5x$
$85.98=2.5x$
$x= \frac{85.98}{2.5}=34.392$≈ 35 weeks

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If we can start saving as early as possible, then 21 weeks of $2.50/week would work for the cheaper price of season-fee and we don't need to adjust the budget. However, if we still want to aim for $85.98 season pass fee, but only have fewer weeks to save, then adjusting budget is necessary. We can perhaps decide not to go bowling every week so we can use the budget for saving instead, or we can alternate between bowling and movie every week. 

Question d)

Using the original budget, we work out a third of $2.50 which is 2.5÷3 = 0.83
It means we have 2.5-0.83 = 1.6 left to save weekly. 

Using the same equation with part b)
$y=35+1.6x$ ⇒ Notice that we adjust the constant 2.5 to 1.6
$85.98 = 35+1.6x$ ⇒ We still aim to save for the cheapest season-pass
$85.98-35=1.6x$
$50.98=1.6x$
$x= \frac{50.98}{1.6}=31.8625$ ≈ 32 weeks

We will have 32 weeks × $0.83 = $26.56 to buy gift for Mother.

Question e)

From information from part a) to part d), there are many different ways to adjust the budget.