Sally paid [tex]$12.50[/tex] for 5 teeny-tiny geraniums and 10 tulip bulbs. Vicki paid [tex]$14.50[/tex] for 7 teeny-tiny geraniums and 11 tulip bulbs. Assume they both shopped at the same home and garden supply store.

Answer the questions below. Write your answer to two decimal places.

a) How much did each geranium cost?

b) How much did each tulip bulb cost?

Let the cost of one teeny-tiny geranium be [tex]$g$[/tex] dollars and the cost of one tulip bulb be [tex]$t$[/tex] dollars.

Sally's purchase gives the equation
[tex]$$
5g + 10t = 12.50.
$$[/tex]
Dividing the equation by 5 to simplify, we obtain
[tex]$$
g + 2t = 2.50.
$$[/tex]
Solving for [tex]$g$[/tex], we have
[tex]$$
g = 2.50 - 2t.
$$[/tex]

Vicki's purchase gives another equation:
[tex]$$
7g + 11t = 14.50.
$$[/tex]
Substitute the expression [tex]$g = 2.50 - 2t$[/tex] into this equation:
[tex]$$
7(2.50 - 2t) + 11t = 14.50.
$$[/tex]
Expanding the left-hand side, we get:
[tex]$$
17.50 - 14t + 11t = 14.50.
$$[/tex]
Combine like terms:
[tex]$$
17.50 - 3t = 14.50.
$$[/tex]
Subtract [tex]$17.50$[/tex] from both sides:
[tex]$$
-3t = 14.50 - 17.50 = -3.00.
$$[/tex]
Divide both sides by [tex]$-3$[/tex]:
[tex]$$
t = \frac{-3.00}{-3} = 1.00.
$$[/tex]

Now substitute [tex]$t = 1.00$[/tex] back into the expression for [tex]$g$[/tex]:
[tex]$$
g = 2.50 - 2(1.00) = 2.50 - 2.00 = 0.50.
$$[/tex]

Thus, to two decimal places:
- The cost of each teeny-tiny geranium is \[tex]$0.50.
- The cost of each tulip bulb is \$[/tex]1.00.