algebraic expressions

1/3x plus twice y Twice y means we multiply y by 2: 2y 1/3x plus twice y 1/3x + 2y

the quotient of 7 and the total of 5 and x The total of 5 and x 5 + x the quotient of 7 and the total of 5 and x 7/(5 + x)

Ana was y years old 7 years ago. Represent her age twenty years from now twenty years from now, means we add 7 years to get to now and another 20 years to get to twenty years from now: y + 7 + 20 y + 27

The cube of x is less than 15 The cube of x means we raise x to the 3rd power: x^3 Less than 15 means we setup the following inequality x^3 < 15

Add r to the difference of s and t, then add q to the result the difference of s and t s - t Add r to the difference of s and t s - t + r Add r to the difference of s and t, then add q to the result s - t + r + q

square root of x times the square root of y square root of x: sqrt(x) square root of y: sqrt(y) square root of x times the square root of y sqrt(x) * sqrt(y)

multiply k by 6q 6qk

7 times a number and 2 is equal to 4 times a number decreased by 8 The phrase a number means an arbitrary variable, let's call it x. x 7 times a number: 7x and 2 means we add 2: 7x + 2 4 times a number 4x decreased by 8 means we subtract 8: 4x - 8 The phrase is equal to means an equation...

twice the product of p q and r The product of p q and r: pqr Twice means we multiply pqr by 2: 2pqr

Divya has 70 rocks. She donates half of the rocks to a science center. Then she collects 3 rocks on each of her nature hikes. Write an expression to represent the number of rocks Divya has after she collects rocks on n nature hikes. For each hike, we have: Start with 70 rocks She donates half...

Kimi has 62 red peppers and g green peppers. Choose the expression that shows how many peppers Kimi has. We add to get the total peppers: 62 + g

Finn has 8 toy cars. Dirk has t times as many toy cars as Finn The phrase times as many means we multiply: 8t

Karen bought a bucket of popcorn at the movies for $5. She also bought some candy for $2 each. Karen has to spend less than $15 on the popcorn and candy. Which inequality can be used to find c, the number of candies that Karen could have bought? Since the candy cost is the product of price and...

product of a number and its reciprocal is increased by 7 The phrase a number means an arbitrary variable, let's call it x: x Its reciprocal means we take the reciprocal of x: 1/x product of a number and its reciprocal: x * 1/x x/x The x's cancel giving us: 1 is increased by 7 means we add...

Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account has a balance of $81. How much did she have in her account to start with? We start with a balance of b. Depositing 41 means we add to the account balance: b + 41 Writing checks for 31 and 13...

the square of the sum of 2a and 3b the sum of 2a and 3b 2a + 3b The square of this sum means we raise 2a + 3b to the 2nd power: (2a + 3b)^2

k add 2 multiply by 6 then subtract 8 k add 2: k + 2 Multiply by 6: 6(k + 2) Then subtract 8: 6(k + 2) - 8

twice the difference between x and 28 is 3 times a number The difference between x and 28: x - 28 Twice the difference means we multiply x - 28 by 2: 2(x - 28) The phrase a number means an arbitrary variable, let's call it x x 3 times a number: 3x The word is means equal to, so we set 2(x -...

6 is one third of a number s A number s is written as s: s One third of a number s means we multiply s by 1/3 s/3 The word is means equal to, so we set s/3 equal to 6 s/3 = 6

the cost of b books at p dollars each Cost = Price * Quantity, so we have: Cost = pb