Translate an english phrase to an algebraic expression
In the last section, we listed many operation symbols that are used in algebra, then we translated expressions and equations into English phrases and sentences. Now we’ll reverse the process. We’ll translate English phrases into algebraic expressions. The symbols and variables we’ve talked about will help us do that.
[link] summarizes them.
Operation
Phrase
Expression
Addition
a plus
b the sum of
and
b
increased by
b b more than
the total of
and
b b added to
Subtraction
minus
b the difference of
and
b
decreased by
b b less than
b subtracted from
Multiplication
times
b the product of
and
b twice
2
a
Division
divided by
b the quotient of
and
b the ratio of
and
b b divided into
Look closely at these phrases using the four operations:
Each phrase tells us to operate on two numbers. Look for the words
of and
and to find the numbers.
Translate each English phrase into an algebraic expression:
ⓐ the difference of
and
ⓑ the quotient of
and
Solution
ⓐ The key word is
difference , which tells us the operation is subtraction. Look for the words
of and
and t o find the numbers to subtract.
ⓑ The key word is “quotient,” which tells us the operation is division.
How old will you be in eight years? What age is eight more years than your age now? Did you add 8 to your present age? Eight “more than” means 8 added to your present age. How old were you seven years ago? This is 7 years less than your age now. You subtract 7 from your present age. Seven “less than” means 7 subtracted from your present age.
Translate the English phrase into an algebraic expression:
ⓐ Seventeen more than
yⓑ Nine less than
Solution
ⓐ The key words are
more than. They tell us the operation is addition.
More than means “added to.”
ⓑ The key words are
less than . They tell us to subtract.
Less than means “subtracted from.”
Translate the English phrase into an algebraic expression:
ⓐ five times the sum of
m and
nⓑ the sum of five times
m and
n .
Solution
There are two operation words—
times tells us to multiply and
sum tells us to add.
ⓐ Because we are multiplying 5 times the sum we need parentheses around the sum of
m and
n ,
This forces us to determine the sum first. (Remember the order of operations.)
ⓑ To take a sum, we look for the words “of” and “and” to see what is being added. Here we are taking the sum
of five times
m and
n .
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?