ATwo quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional.
BTwo quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional.
AYes, see solution.
BYes, see solution.
Practice makes perfect
We want to determine whether the amount of tax collected is proportional to the cost of an item before the tax is added. We know that MegaMart adds 116 of the retail price of each purchase on in tax. Let's start by finding the amounts of tax on purchases of $16, $32, $ 48, and $ 64. Let's use this information to complete the table.
Retail Price ($)
16
32
48
64
Tax Collected ($ )
1/16(16)= 16/16=1
1/16(32)= 32/16=2
1/16(48) = 48/16=3
1/16(64) = 64/16=4
Let's write the relationships for the amount of tax and retail price as ratios in simplest form.
Retail Price ($)
16
32
48
64
Tax Collected ($ )
1
2
3
4
Ratio
16/1=16
32/2=16
48/3=16
64/4=16
Recall that two quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional. In this case, all of the ratios can be simplified to 16. This means that the amount of tax collected is proportional to the cost of an item before tax is added.
Now we want to check whether the amount of tax collected is proportional to the cost of an item after tax has been added. Let's start by finding the cost with tax included for items that cost $16, $32, $ 48, and $ 64. Remember that we found amounts of taxes for these prices in Part A.
Retail Price ($)
16
32
48
64
Tax Collected ($ )
1
2
3
4
Cost Including Tax ($ )
16+1=17
32+2=34
48+3=51
64+4=68
Now let's write each of these total costs as ratios in simplest form.
Retail Price ($)
16
32
48
64
Tax Collected ($ )
1
2
3
4
Cost Including Tax ($ )
17
34
51
68
Ratio
17/1=17
34/2=17
51/3=17
68/4=17
Recall that two quantities are proportional if they have a constant ratio or unit rate. For relationships in which this ratio is not constant, the two quantities are not proportional. In this case, all of the ratios can be simplified to 17, so the amount of tax collected is proportional to the cost of an item after tax has been added.
