Forming Equations from Words Flashcards

All 7 cards in this deck

What is the first step in forming an equation from a worded problem?

Define a letter for the unknown quantity.
e.g. "let $x$ be the number of books on shelf A"

How do you write "7 less than 4 times a number" as an expression?
e.g. call the number $n$

$4n-7$

How do you write three consecutive integers algebraically?
e.g. the smallest is $n$

$n$, $n+1$, $n+2$

What are the steps to form and solve a linear equation from a worded problem?
e.g. shelf A has $x$ books, shelf B has $(3x+1)$ books, and there are 45 books in total

1. Write the total as an expression and equate it to the given total: $x+3x+1=45$
2. Simplify and solve: $4x=44$, so $x=11$
3. Interpret: shelf A has 11 books

True or false? If a tea costs £$t$ and a coffee costs £$c$, then 3 teas and 2 coffees cost £$6tc$.

False.
The total cost is £$3t+2c$ — you multiply each price by its number and add.

How do you form a pair of simultaneous equations from a context?
e.g. 3 teas and 2 coffees cost £7.80; 5 teas and 4 coffees cost £14.20

Choose a letter for each unknown and write one equation for each piece of information: $3t+2c=7.80$ and $5t+4c=14.20$

True or false? If Sam is $x$ years old and Tom is 3 years younger than Sam, then Tom's age is $(x-3)$ years.

True. "3 years younger" means subtract 3 from Sam's age, so Tom is $(x-3)$ years old.