Ian’s monthly allowance is $21. in january he starts saving for a birthday gift in june. each month he saves 2/3 of his allowance. the gift he wants to buy costs $110. will ian have enough money? explain.

He starts saving $ in January to buy a gift in June. (which is 6 months, or 5 months not including June)

Each month he saves 2/3 of his allowance, which is $14.

[his allowance each month is $21, 2/3 of his allowance is $14]

(you multiply 21 by 2/3 = 42/3 = 14)

The gift he wants to buy is $110

x = the number of months

y = total cost

14x = y  

14x = 110    [he saves $14 each month, he wants to have a total of $110 to buy a gift]

Plug in 6 for x in the equation

14(6) = 110

84 = 110   (He is $26 short, so saving either for 5 or 6 months will not get Ian $110)

Ian will not have enough money because he is $26 short for 6 months or $40 short for 5 months. (you can decide whether you want to go by 5 months or 6(including June), sorry for the confusing answer)

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92