IB Mathematics SL 1.8 Systems of linear equations AI SL Paper 1- Exam Style Questions- New Syllabus
Question
A specialty bakery offers cupcakes in three distinct box sizes:
- Small box: Contains 1 cupcake and costs \( \$4.50 \)
- Medium box: Contains 6 cupcakes and costs \( \$23.50 \)
- Large box: Contains 12 cupcakes and costs \( \$44.75 \)
In a single week, the bakery sold a total of 88 boxes, containing 383 cupcakes, and generated a total revenue of \( \$1486 \).
Let \( x \) be the number of small boxes, \( y \) the number of medium boxes, and \( z \) the number of large boxes sold. The relationship for the total number of boxes is: \( x + y + z = 88 \).
(a) Formulate a system of equations in terms of \( x, y, \) and \( z \) to represent:
(i) the total quantity of cupcakes sold.
(ii) the total revenue collected from these sales.
(i) the total quantity of cupcakes sold.
(ii) the total revenue collected from these sales.
(b) Hence, by utilizing your graphic display calculator (GDC), determine the number of medium boxes sold during that week.
Most appropriate topic codes (IB Mathematics: applications and interpretation 2019):
• SL 1.8: Create and use technology to solve systems of linear equations in up to 3 variables — parts (a) and (b)
▶️ Answer/Explanation
(a)
(i) \( x + 6y + 12z = 383 \)
(ii) \( 4.50x + 23.50y + 44.75z = 1486 \)
(b)
Solving the system of equations using a GDC gives:
\( x = 53,\quad y = 15,\quad z = 20 \)
Thus, the number of medium boxes sold is \( \boxed{15} \).