Substitute from Word Problems
You already know that in algebra, variables represent values, and if you know the value, you can substitute the value for the variable in an equation.
The rule of substitution (any values that are equal can be freely substituted for each other) also holds true for word problems.
Many word problems give you an equation and a value for a variable. All you have to do is plug in the value for the variable and solve.
Let's try one of those word problems.
Example:
In an early heat wave, the temperature in Los Angeles reached $95^{\circ}$ Fahrenheit (F). What was the temperature in Celcius (C)? ($F=\dfrac{9}{5}C+32$)
Start with what you know:
$$\eqalign{F&=\dfrac{9}{5}C+32\\F&=95}$$
You can replace the F with (95) and then solve the equation.
$$\eqalign{F&=\dfrac{9}{5}C+32\\(95)&=\dfrac{9}{5}C+32\\-32&\qquad\quad -32\\63&=\dfrac{9}{5}C\\\div\dfrac{9}{5}&\; \div \dfrac{9}{5}\\35&=C}$$
It was $35^{\circ}$ Celcius
Practice Problems:
Substitute from Word Problems Practice
1.
$m=1.50p$
The transit authority uses the formula above to ascertain the relationship between the number of passengers ($p$) and the money earned ($m$) for each bus it owns. If a bus made 900 dollars on Tuesday, how many passengers used the bus?
2.
$A=\dfrac{I}{60}$
The equation above shows the relationship between the number of Indian rupees (I) and American dollars (A). How many Indian rupies is $32 American dollars worth?
3.
The amount of crystals a person ($c$) can find in a treasure game app is related to the amount of minutes ($m$) a person digs for treasure in the game. ($c=3m+9$). If Shannon receives 360 crystals, how many minutes did she dig for?
4.
The temperature in Houston reached a low of 68 degrees Fahrenheit ($F$) on April 6th. What was the temperature in Celcius ($C$)? $F=\dfrac{9}{5}C + 32$
5.
On New Years Eve, the temperature in Montreal reached a low of 23 degrees Fahrenheit ($F$). What was the temperature in Celcius ($C$)? $F=\dfrac{9}{5}C + 32$
6.
On Christmas Eve, the temperature in London reached a low of -15 degrees Celcius ($C$). What was the temperature in Fahrenheit ($F$)? $(F-32)\times\dfrac{5}{9}=C$
7.
On June 19th, the temperature in Orlando reached a high of 40 degrees Celcius ($C$). What was the temperature in Fahrenheit ($F$)? $(F-32)\times\dfrac{5}{9}=C$
8.
A local bank uses an equation to determine how many pens ($p$) to have available each day based on the number of transactions ($n$) every 10 minutes. The formula the bank uses is $p=\sqrt{n-2}+9$. If there are 13 pens available, how many transactions are in each 10 minute period?
9.
A local bank uses an equation to determine how many pens ($p$) to have available each week based on the number of transactions ($n$) every hour. The formula the bank uses is $(p-9)^2+2=n$. If there are 123 transactions from 9:00AM to 10:00AM, how many pens must be available?
10.
How many degrees ($d$) are in $\dfrac{3\pi}{4}$ radians ($r$)? The formula for radians into degrees is given by the formula $r= \dfrac{\pi}{180} \times d$.
11.
How many degrees ($d$) are in $\dfrac{10\pi}{3}$ radians ($r$)? The formula for radians into degrees is given by the formula $r= \dfrac{\pi}{180} \times d$.
12.
How many radians ($r$) are in 315 degrees ($d$)? The formula for radians into degrees is given by the formula $d= \dfrac{180}{\pi} \times r$. Answers in radians may be left in terms of $\pi$.
13.
How many radians ($r$) are in 5 degrees ($d$)? The formula for radians into degrees is given by the formula $d= \dfrac{180}{\pi} \times r$. Answers in radians may be left in terms of $\pi$.
Answer Key:
Test Prep Practice
Substitute from Word Problems Test Prep
1.
$F=9.8m$
The mass ($m$) of an object is related to the force of gravity ($F$) on Earth as shown in the formula above. If the object produced a force of 215.6N, what was the mass of the object?
(A) 23.2
(B) 22
(C) 205.8
(D) 2112.88
2.
$n=2000-5p^2$
A supermarket calculated an equation relating the price of an item ($p$) to the number of times it is purchased in a month ($n$). A specialty tub of ice cream is puchased 875 times in a month, how much does this ice cream probably sell for?
(A) 15
(B) 24
(C) 75
(D) 120
3.
An prestigious blog site attempted to find a connection between the cost of plane tickets with distance travelled. $F$ is the estimated cost of a flight. $d$ is the distance measured in miles. The equation relating the two is listed below. If the cost of a flight is 149 dollars, how far away can a person travel?
$F=50+0.11d$
(A) 900
(B) 1809.09
(C) 90
(D) 66.39
4. Grid in your answer in the boxes below.
$A=\dfrac{\pi}{2}\times(\dfrac{d}{2})^2$
The area ($A$) of a semicircle is related to the diameter of the semicircle ($d$) as shown in the equation above. If the area of a circle is $162\pi$, what is the diameter of the semicircle?
Answer Key: