Forming & Solving Equations Flashcards

All 9 cards in this deck

What are the steps to form and solve an equation from a 'think of a number' problem?

e.g. I multiply my number by 5, then add 7; the answer is 72

1. Call the number $x$ and write the operations: $5x + 7$
2. Set it equal to the answer: $5x + 7 = 72$
3. Solve: $5x = 65$, so $x = 13$

True or false? '5 less than $n$' is written as $5 - n$.

False. It is $n - 5$ — you start from $n$ and take 5 away.

What are the steps to form and solve two simultaneous equations from a cost problem?

e.g. 2 teas and 1 cake cost £5; 1 tea and 1 cake cost £3

1. Let $t$ = cost of a tea, $c$ = cost of a cake: $2t + c = 5$ and $t + c = 3$
2. Subtract to eliminate $c$: $t = 2$
3. Substitute back: $c = 1$, so a tea costs £2 and a cake costs £1

Which angle fact do you use to form an equation from the three angles of a triangle?

e.g. the angles are $x$, $4x$ and $4x - 27$

The angles in a triangle add up to $180°$: $x + 4x + 4x - 27 = 180$.

What are the steps to find the angles of a triangle described in words?

e.g. the largest angle is 4 times the smallest, and the third angle is $27°$ less than the largest

1. Call the smallest angle $x$: the angles are $x$, $4x$, $4x - 27$
2. Set their sum equal to $180$: $9x - 27 = 180$
3. Solve and substitute back: $x = 23$, so the angles are $23°$, $92°$, $65°$

What are the steps to form and solve an equation from the perimeter of a labelled shape?

e.g. a rectangle of width $x$ cm and length $x + 3$ cm has perimeter 26 cm

1. Add all the sides: $2x + 2(x + 3) = 4x + 6$
2. Set equal to the given perimeter: $4x + 6 = 26$
3. Solve: $x = 5$, so the width is 5 cm and the length is 8 cm

How do you form an equation from the area of a labelled rectangle?

e.g. a rectangle with sides $2x$ cm and 5 cm has area 40 cm$^2$

Multiply the side expressions and set the product equal to the given area: $10x = 40$.

True or false? The perimeter of a rectangle with width $x$ and length $x + 7$ is $x + (x + 7)$.

False. The perimeter uses all four sides: $2x + 2(x + 7) = 4x + 14$.

True or false? In a 'show that' question you may just write down the given result without showing the steps.

False. Full working must be seen — every step from the information given to the stated result.