Translate each phrase into an algebraic expression.

1. six times a number minus eleven

• 6 • x – 11

2. the product of eight hundred and a number

• 800 • x

3. the quotient of thirty and the product of ten times a number

• 30 ÷ (10 • x)

4. five times the sum of three and some number

• 5 • (3 + x)

5. half the distance to the school.

• Define x as the distance to the school
•  x ÷ 2

6. In order to encourage recycling, the city is offering five cents for every pound of newspapers collected, twenty-five cents per pound for cans, and ten cents per pound for glass bottles or jars.

a. Write an expression for the total amount earned from recycling.

• define x as the pounds of newspapers collected
• define y as the pounds of cans collected
• define z as the pounds of glass bottles or jars collected
• 5 • x + 25 • y +10 • z

 

b. If Chen brings in ten pounds of newspapers, eight pounds of cans, and two pounds of glass, how much will he receive?

5 • 10 + 25 • 8 +10 • 2 = 50+200+20=270(cents)

7. The volume of a box is given by V = l ⋅ w ⋅ h where l = length, w = width, and h = height. Find the volume of a box if length is 25 cm, width is 13 cm, and height is 4 cm.

• l=25, w=13, h=4
• V= 25•13•4=1300 cm³