SEARCH HOME
 Math Central Quandaries & 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 $\$1500 + \$R.$