Math CentralQuandaries & Queries


Question from Ruby, a student:

This question showed up in one of my Math assignments and nothing on the internet seemed to help me find a way to calculate it.

A certain country has a two-tiered GST system. For the first $\$1500$ of any item, GST is levied at 10% and any amount over $\$1500$ is levied at 15%.
Determine the amounts that give the following GSTs.
a) $\$350$
b) $\$780$

Hi Ruby,

10% of $\$1500$ is $0.10 \times \$1500 = \$150$ and since both of the GST amounts you have are more that $\$150$ the items purchased must have cost more than $\$1500.$

Suppose the GST paid had been $\$450.$ Think of the purchase happening in two steps.

Step 1:

Purchase part of your order for $\$1500$ and pay a GST amount of $0.10 \times \$1500 = \$150.$

Step 2:

Purchase the remainder of your order for $\$R$ and pay 15% GST on this part. The GST you paid in this second step was $\$450 - \$150 = \$300.$ What is the amount $\$R$ if 15% of $\$R$ is $\$300?$

You paid $\$1500 + \$R.$

Now try your problem,

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