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(a) Pete and Maeve are saving to buy an Xbox - Junior Cycle Mathematics - Question 5 - 2017
Question 5
(a) Pete and Maeve are saving to buy an Xbox. (i) Pete has saved €20 to begin with. He saves a further €12 each week. Find the total amount of money Pete w... show full transcript
Worked Solution & Example Answer:(a) Pete and Maeve are saving to buy an Xbox - Junior Cycle Mathematics - Question 5 - 2017
Step 1
(i) Find the total amount of money Pete will have saved after 5 weeks.
Answer
To find Pete's total savings after 5 weeks, start with his initial amount and add the money he saves each week.
Pete's initial savings: €20 Amount saved each week: €12
After 5 weeks, the total savings can be calculated as:
Calculating this gives:
Therefore, Pete will have saved a total of €80 after 5 weeks.
Step 2
Step 3
Step 4
(c) After how many weeks will they have enough money saved to buy the Xbox?
Answer
To determine after how many weeks they will have enough money to buy the Xbox, we need to establish the total contributions from both Pete and Maeve.
Pete contributes one quarter of his total savings: ext{Pete's contribution} = rac{1}{4}(20 + 12n)
Maeve contributes two thirds of her total savings: ext{Maeve's contribution} = rac{2}{3}(15 + 6n)
Setting up the equation:
rac{1}{4}(20 + 12n) + rac{2}{3}(15 + 6n) = 200
Next, let's find a common denominator (which is 12) to simplify:
rac{3}{12}(20 + 12n) + rac{8}{12}(15 + 6n) = 200
Expanding and simplifying:
rac{3(20) + 36n + 8(15) + 48n}{12} = 200
Combining terms gives:
egin{align*}
60 + 120n & = 2400
120n & = 2340
n & = rac{2340}{120} = 19.5
ext{Approximately } 20 ext{ weeks.}
ext{Thus, they will need about 27 weeks.}