Niamh is in a clothes shop and has a voucher which she must use. The voucher gives a €10 reduction when buying goods to the value of at least €35. She also has €50 cash. (a) Write down an inequality in x to show the range of cash that she could spend in the shop. (b) Niamh buys one item of clothing in the shop, using the voucher as she does so. Write an inequality in y to show the range of possible prices that this item could have, before the €10 reduction is applied.

Junior Cycle Mathematics Number Systems: Niamh is in a clothes shop and h

Niamh is in a clothes shop and has a voucher which she must use - Junior Cycle Mathematics - Question 6 - 2015

Question 6

Niamh is in a clothes shop and has a voucher which she must use. The voucher gives a €10 reduction when buying goods to the value of at least €35. She also has €50 c... show full transcript

Worked Solution & Example Answer:Niamh is in a clothes shop and has a voucher which she must use - Junior Cycle Mathematics - Question 6 - 2015

Step 1

Write down an inequality in x to show the range of cash that she could spend in the shop.

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Answer

To determine the range of cash Niamh can spend, we need to consider two points:

Minimum Spend Requirement: Niamh must use her voucher which requires her to spend at least €35. The amount she can spend (x) must therefore satisfy the inequality:

$x \geq 35 - 10$

This simplifies to:

$x \geq 25$
Maximum Cash Available: Niamh has €50 in cash, which means:

$x \leq 50$

Combining these inequalities, we have:

$25 \leq x \leq 50$

Step 2

Niamh buys one item of clothing in the shop, using the voucher as she does so. Write an inequality in y to show the range of possible prices that this item could have, before the €10 reduction is applied.

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Answer

When Niamh buys an item of clothing, we need to account for the voucher reduction. Let's denote the price of the item as y. The price must be at least €35 to qualify for the voucher reduction, and since her maximum cash spending is €50 (after applying the voucher), we can express this with:

Minimum Price Requirement:

$y \geq 35$
Maximum Price Considering Cash Available:

Since after the discount the maximum she can spend is €50, and she gets €10 off, we write:

$y \leq 50 + 10$

This simplifies to:

$y \leq 60$

The combined inequalities for the price of the item are:

$35 \leq y \leq 60$

Niamh is in a clothes shop and has a voucher which she must use - Junior Cycle Mathematics - Question 6 - 2015

Worked Solution & Example Answer:Niamh is in a clothes shop and has a voucher which she must use - Junior Cycle Mathematics - Question 6 - 2015

Write down an inequality in x to show the range of cash that she could spend in the shop.

Niamh buys one item of clothing in the shop, using the voucher as she does so. Write an inequality in y to show the range of possible prices that this item could have, before the €10 reduction is applied.

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