25
you are now on your way to college and need to make some
money decisions. your parents are going to pay for some
necessities but they want to know what you need. you are
budgeting your money for textbooks and trying to decide how
many hardback and paperback textbooks you can afford.
hardback books cost $45 and paperback books cost $20. you
have $440 dollars to spend on textbooks. you know you need to
buy 12 textbooks for the school year. your task is to find out
how many hardback and paperback textbooks you can buy.
20+
a) write a system of equations to represent the situation,
let x = the number of hardback books and y = number of
paperback books
equation 1
equation 2

Equation :  1       45 x +  20 y ≤ 440

Equation :  2         x + y   ≤  12

Step-by-step explanation:

Let x = the number of hardback books

and y = number of  paperback books

Cost of 1 hardback book = $45

⇒Cost of x hardback book = $45  times x  =  45 x

Cost of 1 paperback book = $20

⇒Cost of y paperback book = $20  times y  = 20 y

Total allowance for the books

=   Expenditure on hardback books +  Expenditure on paperback books

=    45 x +  20 y

Also, the total number of books bought = x+ y

So, according to the question:

 45 x +  20 y ≤ 440

and      x + y   ≤  12

Above system of equation is the desired system to represent the given situation.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.