Introduce variables for the price of a necklace and a pair of earrings.
Necklace: $15.75 Pair of earrings: $25.50
Practice makes perfect
We are asked to use Cramer's Rule to find the price of a necklace and a pair of earrings.
To do this, we need to introduce variables and set up an equation system.
Description
Variable
Price of a necklace
n
Price of a pair of earrings
e
Let's use these variables to write equations expressing the information given in the question.
Description
Equation
For 3 necklaces and 2 pairs of earrings Alana paid $98.25.
3n + 2e=98.25
For 2 necklaces and 4 pairs of earrings Petra paid $133.50.
2n + 4e=133.50
We found a system of equations in the two unknowns n and e.
3n+ 2e= 98.25 2n+ 4e= 133.50
To use Cramer's Rule, we need the coefficient matrix of the system.
C=
3 & 2
2 & 4
If the determinant of the coefficient matrix |C| is different from zero, Cramer's Rule tells us how to find the solution to our system by using determinants.
n=98.25 & 2 133.50 & 4/|C| and e= 3 & 98.25 2 & 133.50/|C|
Let's start by calculating |C|.
