3.08 Applications of simultaneous equations
Interactive practice questions
When comparing some test results Christa noticed that the sum of her Geography test score and Science test score was $172$172, and that their difference was $18$18.
Given that her Geography score is $x$x and her Science score is $y$y and she scored higher for the Geography test:
Use the sum of the test scores to form an equation. We will refer to this as equation (1).
Use the difference of the test scores to form an equation. We will refer to this as equation (2).
Use these two equations to find her Geography score.
Now find her Science score.
Toby's piggy bank contains only $5$5c and $10$10c coins. If it contains $48$48 coins with a total value of $\$3.45$$3.45, find the number of each type of coin.
Let $x$x and $y$y be the number of $5$5c and $10$10c coins respectively. We will create two equations then solve them simultaneously.
The two equations $y=3x+35$y=3x+35 and $y=4x$y=4x represent Laura’s living expenses and income from work respectively.
Oprah invested $\$16000$$16000 in total in two stocks $A$A and $B$B. In one year, the investment in stock $A$A made a $14%$14% return, while the investment in stock $B$B fell by $6%$6%. The total annual interest from both stocks was $\$700$$700.
Let $x$x and $y$y be the amounts, in dollars, that she invested in stocks $A$A and $B$B respectively.