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Solutions
33 Videos

Translate each sentence into an algebraic expression.

a) three more than five times a number

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Q1a

Translate each sentence into an algebraic expression.

b) five less than one-third of a value

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Q1b

Translate each sentence into an algebraic expression.

c) one number increased by four times another number

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Q1c

Translate each sentence into an algebraic expression.

d) a value decreased by the fraction three quarters

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Q1d

Translate each sentence into an equation. Tell how you are assigning the variables in each.

Three times a number, increased by four, is one half the same number, decreased by one.

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Q2a

Translate each sentence into an equation. Tell how you are assigning the variables in each.

Emma's age increased by five is twice Julia's age, decreased by seven.

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Q2b

Translate each sentence into an equation. Tell how you are assigning the variables in each.

Azula has nickels and quarters that total $1.65 in her piggy bank.

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Q2c

a) Use a graphing calculator or The Geometer ’s Sketchpad® to find the point of intersection of the lines.

`y=4x+1`

and `y=-\dfrac{1}{4}x-2`

If necessary, round your answer to the nearest hundredth.

b) Use a graphing calculator or The Geometer ’s Sketchpad® to find the point of intersection of the lines.

`y = 5x+3`

and `y=-\dfrac{1}{5}x-1`

If necessary, round your answer to the nearest hundredth.

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Q3

Solve each linear system using the method of substitution. Check each solution.

` x+y=5`

`y=x-3`

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Q4a

Solve each linear system using the method of substitution. Check each solution.

`x-y=7`

`y=-x+5`

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Q4b

Solve each linear system using the method of substitution. Check each solution.

`2x+y=1`

`x-3y=4`

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Q4c

Solve each linear system using the method of substitution. Check each solution.

`3x-4y=19`

`x+2y=3`

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Q4d

Solve each linear system using the method of substitution. Check each solution.

`x+3y=15`

`4x-y=8`

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Q4e

Solve each linear system using the method of substitution. Check each solution.

`5x-y=4`

`-x+3y = 2`

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Q4f

There are 28 fish in an aquarium. There are eight more goldfish than neon tetras in the aquarium. How many goldfish are in the aquarium? How many neon tetras are in the aquarium?

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Q5

Maddy would like to rent a digital camera this weekend. One company charges a flat rate of $75/day. A second company charges $35/day plus $5/h.

a) Write two equations to represent the information.

b) Solve the linear system to find the number of hours for which the cost of renting a digital camera is the same for both companies.

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Q6

Which is *not* an equivalent equation for ` 6x+3y = 15`

a) `2x+y = 5`

b) `12x +6y = 30`

c) `9x +6y = 18`

d) `x+\dfrac{1}{2}y = \dfrac{5}{2}`

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Q7

If ` y = 4x-5`

and `5y=kx-25`

are equivalent linear equations, what is the value of `k`

?

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Q8a

If `y =6x+2`

and `4y=24x +k`

are equivalent linear equations, what is the value of `k`

?

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Q8b

The total number of graphing calculators and scientific calculators in Carly's classroom is 14.

a) State how you will assign variables.

b) Write an equation to represent this situation. Then, write an equivalent linear equation.

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Q9

Find the point of intersection of each pair of lines using the method of elimination. Check each solution.

` x+y=5`

`3x-y=11`

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Q10a

Find the point of intersection of each pair of lines using the method of elimination. Check each solution.

`5x+3y = 9`

`2x-3y = 12`

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Q10b

Find the point of intersection of each pair of lines using the method of elimination. Check each solution.

`x+3y = 11`

`-x +4y = -4`

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Q10c

` 4x +5y = 18`

`4x +y = 2`

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Q10d

Solve each linear system. Cheek each solution.

` 5x +4y = 20`

`4x - 3y = 16`

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Q11a

Solve each linear system. Cheek each solution.

`5a +3b = 4`

` 2a - 4b = -1`

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Q11b

Solve each linear system. Cheek each solution.

`0.3m +0.2n = 0.8`

`0.5m -0.3n = 0.7`

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Q11c

Solve each linear system. Cheek each solution.

`2(x+3) + 4(y-2) = 10`

`3(x-2) + 5(y+2) = 8`

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Q11d

One type of fertilizer has 40% nitrogen and the second type of fertilizer has 20% nitrogen. How much of each type of fertilizer should be mixed to make 800 kg of fertilizer that has 25% nitrogen?

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Q12

The RED Cab Service charges $6 plus $2.00/km travelled. YELLOW’s Taxi Service charges $4 plus $2.50/km.

a) For what distance is the charge the same using either taxi company?

b) For what number of kilometres would you choose the RED Cab Service?

c) For what number of kilometres would you choose YELLOW's Taxi Service?

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Q13

There are 52 books in Lara Jean's library. There are 28 more fiction books than non-fiction books.

a) How many fiction books are in Lara Jean’s library?

b) How many non-fiction books are in Lara Jean’s library?

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Q14

Mai invests her summer earnings of $2440. She invests part of the money at 8%/year, and the rest at 7.5%/year. After one year, these investments earn $193 in simple interest. How much did she invest at each rate?

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Q15

A speedboat took 3 h to travel a distance of 60 km up a river, against the current. The return trip took 2 h. Find the average speed of the boat in still water and the speed of the current.

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Q16