 # Problem of the Week Problem A and Solution Saving Up

## Problem

Fionnlay earns $$\8$$ each week by walking the neighbour’s dog. Starting in the second week, Fionnlay earns an extra $$\3$$ by helping maintain the community garden every other week. He is saving all of his earnings for a bicycle, which costs $$\157$$. He will also need a helmet which costs $$\24$$, a bike horn which costs $$\16$$, and a bike light which costs $$\9$$. All prices include taxes. Fionnlay keeps track of the money he has earned.

1. How much money will Fionnlay have saved after $$8$$ weeks?

2. How much money will Fionnlay have saved after $$15$$ weeks?

3. How long will it take him to save enough money to buy the bike and its accessories? ## Solution

One way to solve this problem is to create a table that records the total that Fionnlay has saved each week. In the odd-numbered weeks, the total will increase by $$\8$$. In the even-numbered weeks, the total will increase by $$\8 + \3 = \11$$.

We will also need to know how much money Fionnlay needs to save by calculating the total cost of the bike and its accessories. We can do this by adding $$\157 + \24 + \16 + \9 = \206$$.

Week Increase (in $) Total Savings (in$)
$$1$$ $$8$$ $$8$$
$$2$$ $$11$$ $$19$$
$$3$$ $$8$$ $$27$$
$$4$$ $$11$$ $$38$$
$$5$$ $$8$$ $$46$$
$$6$$ $$11$$ $$57$$
$$7$$ $$8$$ $$65$$
$$8$$ $$11$$ $$76$$
$$9$$ $$8$$ $$84$$
$$10$$ $$11$$ $$95$$
$$11$$ $$8$$ $$103$$
$$12$$ $$11$$ $$114$$
$$13$$ $$8$$ $$122$$
$$14$$ $$11$$ $$133$$
$$15$$ $$8$$ $$141$$
$$16$$ $$11$$ $$152$$
$$17$$ $$8$$ $$160$$
$$18$$ $$11$$ $$171$$
$$19$$ $$8$$ $$179$$
$$20$$ $$11$$ $$190$$
$$21$$ $$8$$ $$198$$
$$22$$ $$11$$ $$209$$

Using the table, we can now answer the questions.

1. Fionnlay will have saved $$\76$$ after $$8$$ weeks.

2. Fionnlay will have saved $$\141$$ after $$15$$ weeks.

3. Fionnlay will need $$22$$ weeks to save enough money for the bike and its accessories.