mark decided to improve his yard by planting hostas and geraniums. he can spend $100 on the plants. Hostas cost $9.75 each and geraniums cost $6.50.

Question

a) write an equation to represent all possible number of plants that mark can buy.

b) what is the greatest amount of hostas mark can buy?

c) if mark buys 5 hostas, how many geraniums can he buy?

Answer 1

a) If we let x = # of hostas that Mark can buy and y = # of geraniums Mark can buy, and he has $100 to spend, we can write an equation as follows:

$9.75*x + $6.50*y ≤ $100 (the inequality assumes he can spend less than $100 on plants, if he desires)

b) This part is intuitive. If Mark wants to buy as many hostas as possible, how many geraniums should he buy? (hint: zero). Using our equation from part (a):

$9.75*x + $6.50*(0) = $100 (we use the equal sign now that we know we want to buy as many as possible)

$9.75*x = $100

x = 10.26, we cannot buy part of a plant so we must round down to the nearest whole number

x = 10 hostas

c) Again, we can use our equation from part (a). This time we know the value of x, and we are solving for y.

$9.75*(5) + $6.50*y = $100

$48.75 + $6.50*y = $100

$6.50*y = $51.25

y = 7.88, again we cannot buy part of plant so we round down to the nearest whole number

y = 7 geraniums