smc-3084-40-Multi-Step problems

Number and Algebra, NAP-J2-42 SA

Bert and Ernie are standing in a line, waiting to go into their classroom.

There are:

9 people between Bert and Ernie.
14 people in front of Bert including Ernie.
20 people behind Ernie including Bert.

In total, how many people are in the line?

Show Answers Only

`25`

Show Worked Solution

`text(The line-up will be:)`

`text(10 people → Bert → 9 people → Ernie → 4 people)`

`:.\ text(Total people in line)`

`= 10 + 1 + 9 + 1 + 4`

`= 25`

Number and Algebra, NAP-J2-33

A cricket kit has white, pink and red cricket balls.

There are:

3 more white balls than pink
7 fewer pink balls than red
15 red balls

How many balls, in total, are in the kit?

`19`	`24`	`25`	`34`	`39`

Show Answers Only

`34`

Show Worked Solution

`text{15 red balls (given)}`

`=> 15 – 7 = 8\ text(pink balls)`

`=> 8 + 3 = 11\ text(white balls)`

`:.\ text(Total balls)`	`= 15 + 8 + 11`
	`= 34`

Number and Algebra, NAP-B2-40 SA

Peter sets up a fruit stall outside his house and sells oranges, pears and plums.

The table below shows the price of each fruit.

Peter sold 12 pieces of fruit and was paid $28.

Peter received $8 for all the pears he sold.

How many plums did Peter sell?

Show Answers Only

`6\ text(plums)`

Show Worked Solution

`text(Pears sold)`	`=$8 -: 2`
	`=4`

`=>\ text(The other 8 pieces were sold for $20)`

`text(Testing some guesses for the other 8 pieces:)`

`text(If 5 plums and 3 oranges,)`

`text(C)text(ost) = (5 xx3) + (3 xx 1) = $18\ \ text{(too low)}`

`text(If 6 plums and 2 oranges,)`

`text(C)text(ost) = (6 xx3) + (2 xx 1) = $20\ \ text{(correct)}`

`=>\ text(Peter sold a total of 6 plums.)`

Number and Algebra, NAP-B2-36

Penny has 5 birds that each eat 30 grams of bird food a day.

She has 6kg of bird food.

How many days will her bird food last for?

`4\ text(days)`	`20\ text(days)`	`40\ text(days)`	`200\ text(days)`

Show Answers Only

`40\ text(days)`

Show Worked Solution

`text(Bird food consumption per day)`

`=5 xx 30`

`= 150\ text(g)`

`:.\ text(Number of days the bird food will last)`

`= 6\ text(kg) -: 150\ text(g)`

`= 6000 -: 150`

`= 40\ text(days)`

Number and Algebra, NAP-H2-34 SA

Bonnie and Clyde ate 43 cherries between them.

Bonnie ate 9 less cherries than Clyde.

How many cherries did Bonnie eat?

Show Answers Only

`17\ text(cherries)`

Show Worked Solution

`text(Strategy 1:)`

`text(Consider the possible splits,)`

`22 – 21:\ text(Bonnie eats 1 less)`

`23 – 20:\ text(Bonnie eats 3 less`

`vdots`

`26 – 17:\ text(Bonnie eats 9 less)`

`:.\ text(Bonnie eats 17.)`

`text(Strategy 2:)`

`text(Let)\ \ c = text(number of cherries Bonnie eats)`

`=> c + 6 =\ text(number of cherries Clyde eats)`

`c + c + 9`	`= 43`
`2c`	`= 34`
`:. c`	`= 17`

Number and Algebra, NAP-H2-13

Michelle, Lucy, Clare and Steph are sisters.

The years they were born are recorded in the table below.

Who is the second youngest sister?

`text(Michelle)`	`text(Lucy)`	`text(Clare)`	`text(Steph)`

Show Answers Only

`text(Lucy)`

Show Worked Solution

`text(The order from oldest to youngest is:)`

`text{Clare (1977), Michelle (1978), Lucy (1987), Steph (1988).}`

`:.\ text(Lucy is the second youngest.)`

Number and Algebra, NAP-D2-37 SA

An AFL squad of 38 players were voting for a captain.

Each player had one vote and had to vote for Harrison, Patrick or Charles.

Harrison got 4 more votes than Patrick.

Harrison got 3 more votes than Charles.

How many votes did Harrison get?

Show Answers Only

`15`

Show Worked Solution

`text(Solution 1:)`

`text(By trial and error)`

`text(Harrison gets the most votes → must be more than 13)`

`text(Consider Harrison gets 15 votes)`

`text(→ Patrick gets 11 and Charles gets 12)`

`text(→ Total votes = 15 + 11 +12 = 38)`

`text{Solution 2 (using algebra):}`

`text(Let)\ \ \ H`	`=\ text(votes for Harrison)`
`P`	`=\ text(votes for Patrick)`
`C`	`=\ text(votes for Charles)`

`text(Total votes)`	`= H + P + C`
`38`	`= H + (H – 4) + (H – 3)`
	`= 3H – 7`
`3H`	`= 45`
`H`	`= 15`

`:.\ text(Harrison got 15 votes.)`