Kevin has saved €20 - Junior Cycle Mathematics - Question 8 - 2012
Question 8
Kevin has saved €20. He gets €7 a week for doing jobs at home. He spends €2 on sweets every week and saves the rest in a piggybank.
(a) How much money has he saved ... show full transcript
Worked Solution & Example Answer:Kevin has saved €20 - Junior Cycle Mathematics - Question 8 - 2012
Step 1
How much money has he saved at the end of week 1?
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Answer
At the end of week 1, Kevin saves €5. This is calculated as follows: he starts with €20 and receives €7 for the week. After spending €2 on sweets, the amount saved is €7 - €2 = €5. So, at the end of week 1, he has €20 + €5 = €25.
Step 2
Complete the table to show how his savings grow in the first five weeks.
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The filled table for the first five weeks is as follows:
Week 1
Week 2
Week 3
Week 4
Week 5
€25
€30
€35
€40
€45
This represents Kevin's savings after accounting for his weekly income and expenses.
Step 3
Write down a formula (in words) to represent the amount he has saved at the end of each week.
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The formula to represent the amount saved at the end of each week can be articulated as: "The amount saved at the end of week n is equal to €5 multiplied by the week number plus €20."
Step 4
Kevin would like to buy a mobile phone costing €100. Use your formula to find out how many weeks he needs to save, to have enough money to buy the phone.
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Answer
To find out how many weeks he needs to save, we set the formula equal to €100:
[ 5n + 20 = 100 ]
Solving for n gives:
[ 5n = 100 - 20 ]
[ 5n = 80 ]
[ n = 16 ]
Kevin needs to save for 16 weeks.
Step 5
Kevin stops buying the sweets after 5 weeks. How much can he save each week after that?
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After 5 weeks, Kevin no longer spends €2 on sweets. Therefore, he will save the entire €7 he earns weekly, which amounts to €7.
Step 6
Do you agree with Kevin? Explain your answer.
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Yes, I agree with Kevin. After 13 weeks, at a saving rate of €7 per week without sweet purchases, he will have saved:
[ 7 \times 13 = €91 ]
Including the amount saved in the previous weeks, he has sufficient funds, and with his additional savings, he can buy the phone earlier.
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