Work out the normal price in the second shop ?

2 shops are selling the same hoover. in the first shop the customer pays £7.25 per month for 13 months.
in the second shop the customer gets 35% discount on the shops normal price. with these offers the customer pays the same amount in total for the hoover.

1 Answer
Tony B
Jun 24, 2018

Normal price in the second shop is #£146.54# to 2 decimal places.

Explanation:

Shop 1 #->13xx£7.25 = £94.25#

Set the original price as #x# and drop the £ sign

Shop 2 #->x-35/100x = 94.25#

Lets look at Shop 2 another way.

If there was 35% discount then what was paid was 100%-35%=65%

So we have: #65/100x=94.25#

Multiply both sides by .#color(red)(100/65)#

#color(green)(65/100x=94.25 color(white)("dddd")->color(white)("dddd")65/100color(red)(xx100/65)xx x=95.25color(red)(xx100/65))#

#x=146.53846...#

#x=£146.54# rounded to 2 decimal places
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Foot note")#

Paying over a period usually costs more (interest). So perhaps the first shop would be a better buy if you paid in full. That way you do not pay interest.

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