Problem Solving with Equations Flashcards

All 5 cards in this deck

When an equation formed from a context is quadratic, how do you decide which root to use?

Reject any root that is impossible in the context, such as a negative length or a negative number of objects.

True or false? Once you have solved your equation and found $x$, the problem is finished.

False.
You must substitute $x$ back to find the quantity the question actually asks for.

What are the steps to solve a context problem with two unknowns?
e.g. 2 pens and 1 ruler cost £5; 1 pen and 1 ruler cost £3

1. Define letters and write two equations: $2p+r=5$, $p+r=3$
2. Eliminate one variable and solve: subtracting gives $p=2$
3. Substitute back and interpret: $r=1$, so a pen costs £2 and a ruler £1

What must you include with the final answer to a context problem?

The units and a clear statement of the quantity asked for.
e.g. "cost of one tea = £1.40"

How can you check a solution to an equation you formed from a worded problem?

Substitute the value back into the original situation and check it gives the stated total.