Equasions Ineq and Vics strategy guide p. 63 number 7 & 9

[sanyu4]

For #7: What is meant by "by what factor", Per example given in the answer choice, when "b" = 2, I don't understand why I would put the new doubled cost of 256 divided by 16 the old cost, why not 16/256?

For #9: Per answer, I understand how we get to square rt of 2/2 to sq rt of 3. I do not understand why you have to then solve for x in the next step? Is there an alternative explanation for this?

Thank you
Sarah

[jnelson0612]

For #7: What is meant by "by what factor", Per example given in the answer choice, when "b" = 2, I don't understand why I would put the new doubled cost of 256 divided by 16 the old cost, why not 16/256?

For #9: Per answer, I understand how we get to square rt of 2/2 to sq rt of 3. I do not understand why you have to then solve for x in the next step? Is there an alternative explanation for this?

Thank you
Sarah

Factor means by what are you multiplying the original number to get to the new number? For example, if you are making $100K this year and your salary increases by a factor of 4, you will be making $400K.

For #9, I suggest you plug in real numbers (pick some small easy ones) and see how things change from the first scenario to the second. Let us know if you need more help.