MIP1502 ASSIGNMENT 3 2026
DUE 10 JULY 2026
QUESTION 1
You are helping a Grade 6 mathematics club prepare packs of pattern cards for a
school fundraising activity. A printing shop charges a fixed setup fee of R30, plus R6 per
pack printed. The club sells each pack for R10.
Let 𝒏𝒏 represent the number of packs printed and sold. 1.1 Write the expressions, in
simplified form, for the following: 1.1.1 the total printing cost, 𝐶𝐶(𝑛𝑛); (1) 1.1.2 the total
income, 𝐼𝐼(𝑛𝑛); (1)
1.1.1 The total printing cost, C(n)C(n)
C(n) = 6n+30C(n) = 6n + 30
nn = number of packs printed
R6 = variable cost per pack
R30 = fixed cost setup/printing costs
1.1.2 The total income, I(n)I(n)
Let say each pack is sold at a certain price. From the profit function context, if each
pack sells for R10 deduced from the profit equation
I(n) =10nI (n) = 10n
,1.1.3 The profit, P(n)P(n)
Profit is income minus cost:
P(n) = I(n) −C(n)P(n) = I(n)− C(n)P(n) = 10n− (6n+30)P(n) = 10n −(6n+30) P(n) =
4n−30P(n) = 4n − 30
1.2 Evaluate P(12)P(12) and interpret your answer in one complete sentence.
P(12) = 4(12)−30P(12) = 4(12)−30P(12) = 48−30P(12) = 48− 30P (12)= 18P (12) = 18
If the club sells 12 packs, they will make a profit of R18.
1.3 Explain the difference between an algebraic expression and an algebraic
equation. Use P(n)P(n) and P(n)=50P(n)=50 in your explanation.
An algebraic expression is a mathematical phrase that contains numbers, variables, and
operations but does not contain an equals sign. It simply represents a value. For
example, P(n)=4n−30P(n)=4n−30 is an expression, it tells us how to calculate profit but
does not state what the profit equals.
An algebraic equation, on the other hand, is a statement that two expressions are equal
and contains an equals sign (=)(=). It can be solved to find the value of the variable. For
example, P(n)=50P(n)=50 is an equation because it states that the profit expression
equals 50, allowing us to solve for nn.
, 1.4 Solve P(n)=50P(n)=50. Check your answer by substitution and interpret the
result in the fundraising context.
P(n)= 50P(n) = 504n−30 = 504n−30 = 504n = 804n = 8 0n = 20n = 20
Check by substitution:
P(20) = 4(20)−30P(20) = 4(20)−30P(20) = 80−30P(20) = 80−30P(20)=50✓P(20) = 50✓
The club must sell 20 packs to make a profit of exactly R50.
1.5 The club wants to make at least R100 profit. Write an inequality, solve it, and
state the minimum whole number of packs the club must sell.
Inequality:
P(n)≥ 100P(n)≥1004n− 30≥1004n− 30≥ 100
4n≥1304n≥ 130n≥ 32.5n ≥32.5
Since the club cannot sell half a pack, the minimum whole number of packs is
N =33n = 33
P(33)= 4(33)− 30 = 132−30 = 102≥ 100P(33) = 4(33)−30 = 132−30 = 102≥ 100
DUE 10 JULY 2026
QUESTION 1
You are helping a Grade 6 mathematics club prepare packs of pattern cards for a
school fundraising activity. A printing shop charges a fixed setup fee of R30, plus R6 per
pack printed. The club sells each pack for R10.
Let 𝒏𝒏 represent the number of packs printed and sold. 1.1 Write the expressions, in
simplified form, for the following: 1.1.1 the total printing cost, 𝐶𝐶(𝑛𝑛); (1) 1.1.2 the total
income, 𝐼𝐼(𝑛𝑛); (1)
1.1.1 The total printing cost, C(n)C(n)
C(n) = 6n+30C(n) = 6n + 30
nn = number of packs printed
R6 = variable cost per pack
R30 = fixed cost setup/printing costs
1.1.2 The total income, I(n)I(n)
Let say each pack is sold at a certain price. From the profit function context, if each
pack sells for R10 deduced from the profit equation
I(n) =10nI (n) = 10n
,1.1.3 The profit, P(n)P(n)
Profit is income minus cost:
P(n) = I(n) −C(n)P(n) = I(n)− C(n)P(n) = 10n− (6n+30)P(n) = 10n −(6n+30) P(n) =
4n−30P(n) = 4n − 30
1.2 Evaluate P(12)P(12) and interpret your answer in one complete sentence.
P(12) = 4(12)−30P(12) = 4(12)−30P(12) = 48−30P(12) = 48− 30P (12)= 18P (12) = 18
If the club sells 12 packs, they will make a profit of R18.
1.3 Explain the difference between an algebraic expression and an algebraic
equation. Use P(n)P(n) and P(n)=50P(n)=50 in your explanation.
An algebraic expression is a mathematical phrase that contains numbers, variables, and
operations but does not contain an equals sign. It simply represents a value. For
example, P(n)=4n−30P(n)=4n−30 is an expression, it tells us how to calculate profit but
does not state what the profit equals.
An algebraic equation, on the other hand, is a statement that two expressions are equal
and contains an equals sign (=)(=). It can be solved to find the value of the variable. For
example, P(n)=50P(n)=50 is an equation because it states that the profit expression
equals 50, allowing us to solve for nn.
, 1.4 Solve P(n)=50P(n)=50. Check your answer by substitution and interpret the
result in the fundraising context.
P(n)= 50P(n) = 504n−30 = 504n−30 = 504n = 804n = 8 0n = 20n = 20
Check by substitution:
P(20) = 4(20)−30P(20) = 4(20)−30P(20) = 80−30P(20) = 80−30P(20)=50✓P(20) = 50✓
The club must sell 20 packs to make a profit of exactly R50.
1.5 The club wants to make at least R100 profit. Write an inequality, solve it, and
state the minimum whole number of packs the club must sell.
Inequality:
P(n)≥ 100P(n)≥1004n− 30≥1004n− 30≥ 100
4n≥1304n≥ 130n≥ 32.5n ≥32.5
Since the club cannot sell half a pack, the minimum whole number of packs is
N =33n = 33
P(33)= 4(33)− 30 = 132−30 = 102≥ 100P(33) = 4(33)−30 = 132−30 = 102≥ 100
