smc-693-40-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?

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`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?

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`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)`

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`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?

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`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.)`