A shop sells matching hats and scarves. The scarves cost 1.5 times as much as the hats. Write two patterns that could represent the costs of 1, 2, 3, 4, and 5 hats and scarves. List the first 5 terms of each pattern. Then explain how to find the cost of 6 hats and scarves, using the patterns you wrote. Show your work.

Hello!
It is not that clear whether you need costs of hats and scarves separated or combined. Let's make all.
We don't know the price of a hat, and should imagine it. Let it be $10. Then one scarf will cost 1.5*$10=$15, and a pair will cost $10+$15=$25. The prices for several items will be as follows:
Number of pairs   Cost of hats   Cost of scarves   Cost of pairs1                          10                15                      252                          20                30                      503                          30                45                      754                          40                60                     1005                          50                75                     125
The cost of several hats follows the rule "add 10", of scarves "add 15" and of pairs "add 25" (all that numbers are not surprising and coincide with the prices of one item). Therefore to find the cost for the next quantity, 6, we need to follow the same rules:
6 hats      cost    50+10=60($),6 scarves cost    75+15=90($),6 pairs     cost  125+25=150($).

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