Question

systems of linear equations
guided and independent practice
example 1
kevin would like to buy 10 bouquets. the standard
bouquet costs $7, and the deluxe bouquet costs $12. he
can only afford to spend $100. how many of each type
can he buy?
created equations here:
solution:
example 2
a hot air balloon is 10 meters above the ground and rising
at a rate of 15 meters per minute. another balloon is 150
meters above the ground and descending at a rate of 20
meters per minute. when will the two balloons meet?
created equations here:
solution:

Explanation:

Example 1

Step1: Define variables

Let $x$ = number of standard bouquets, $y$ = number of deluxe bouquets.

Step2: Set up total count equation

Total bouquets: $x + y = 10$

Step3: Set up total cost equation

Total cost: $7x + 12y = 100$

Step4: Isolate $x$ from count equation

$x = 10 - y$

Step5: Substitute into cost equation

$7(10 - y) + 12y = 100$
$70 - 7y + 12y = 100$
$70 + 5y = 100$

Step6: Solve for $y$

$5y = 100 - 70 = 30$
$y = \frac{30}{5} = 6$

Step7: Solve for $x$

$x = 10 - 6 = 4$

Step1: Define variables

Let $t$ = time in minutes when balloons meet, $h$ = height in meters when they meet.

Step2: Rising balloon height equation

Height of first balloon: $h = 10 + 15t$

Step3: Descending balloon height equation

Height of second balloon: $h = 150 - 20t$

Step4: Set heights equal

$10 + 15t = 150 - 20t$

Step5: Solve for $t$

$15t + 20t = 150 - 10$
$35t = 140$
$t = \frac{140}{35} = 4$

Answer:

Kevin can buy 4 standard bouquets and 6 deluxe bouquets.

---

Example 2