The cost of a school shirt is sh.9000 more than the cost of a school short. A school short costs two thirds…

Question

The cost of a school shirt is sh.9000 more than the cost of a school short. A school short costs two thirds the cost of a school T-shirt. The total cost of the three items is sh.51,000. (a) Calculate the cost of a school T-shirt. (b) Find the cost price of a school shirt

ScanSolve AI Tutor · Accepted Answer

a) Calculate the cost of a school T-shirt.

Define variables based on the problem statement.
Let $S$ be the cost of a school shirt.
Let $H$ be the cost of a school short.
Let $T$ be the cost of a school T-shirt.
Formulate equations from the given information.
From "The cost of a school shirt is sh.9000 more than the cost of a school short":
$S = H + 9000 \quad (1)$
From "A school short costs two thirds the cost of a school T-shirt":
$H = \frac{2}{3} T \quad (2)$
From "The total cost of the three items is sh.51,000":
$S + H + T = 51000 \quad (3)$
Substitute equation (2) into equation (1) to express $S$ in terms of $T$ .
$S = \left(\frac{2}{3} T\right) + 9000 \quad (4)$
Substitute equations (2) and (4) into equation (3) to form an equation with only $T$ .
$\left(\frac{2}{3} T + 9000\right) + \left(\frac{2}{3} T\right) + T = 51000$
Solve the equation for $T$ .
Combine the terms with $T$ :
$\frac{2}{3} T + \frac{2}{3} T + T = 51000 - 9000$ $\left(\frac{2}{3} + \frac{2}{3} + \frac{3}{3}\right) T = 42000$ $\frac{7}{3} T = 42000$
Multiply both sides by $\frac{3}{7}$ :
$T = 42000 \times \frac{3}{7}$ $T = 6000 \times 3$ $T = 18000$
The cost of a school T-shirt is sh.18,000.

b) Find the cost price of a school shirt.
Calculate the cost of a school short ( $H$ ) using the value of $T$ from part (a).
$H = \frac{2}{3} T$ $H = \frac{2}{3} \times 18000$ $H = 2 \times 6000$ $H = 12000$
The cost of a school short is sh.12,000.
Calculate the cost of a school shirt ( $S$ ) using the cost of the short.
$S = H + 9000$ $S = 12000 + 9000$ $S = 21000$
The cost of a school shirt is sh.21,000.

Final Answer:

a) The cost of a school T-shirt is $\boxed{\text{sh.18,000}}$ .

b) The cost price of a school shirt is $\boxed{\text{sh.21,000}}$ .

2 zimekamilika. Zimebaki 3 leo — tuma inayofuata.

The cost of a school shirt is sh.9000 more than the cost of a school short. A school short costs two thirds the cost of a school T-shirt. The total cost of the three items is sh.51,000. (a) Calculate the cost of a school T-shirt. (b) Find the cost price of a school shirt

Step-by-step solution

Define variables based on the problem statement.

Formulate equations from the given information.

Substitute equation (2) into equation (1) to express $S$ in terms of $T$ .

Substitute equations (2) and (4) into equation (3) to form an equation with only $T$ .

Solve the equation for $T$ .

Calculate the cost of a school short ( $H$ ) using the value of $T$ from part (a).

Calculate the cost of a school shirt ( $S$ ) using the cost of the short.

Still stuck on this one?

More Mathematics Questions

The cost of a school shirt is sh.9000 more than the cost of a school short. A school short costs two thirds the cost of a school T-shirt. The total cost of the three items is sh.51,000. (a) Calculate the cost of a school T-shirt. (b) Find the cost price of a school shirt

Step-by-step solution

Define variables based on the problem statement.

Formulate equations from the given information.

Substitute equation (2) into equation (1) to express SSS in terms of TTT.

Substitute equations (2) and (4) into equation (3) to form an equation with only TTT.

Solve the equation for TTT.

Calculate the cost of a school short (HHH) using the value of TTT from part (a).

Calculate the cost of a school shirt (SSS) using the cost of the short.

Still stuck on this one?

More Mathematics Questions

Substitute equation (2) into equation (1) to express $S$ in terms of $T$ .

Substitute equations (2) and (4) into equation (3) to form an equation with only $T$ .

Solve the equation for $T$ .

Calculate the cost of a school short ( $H$ ) using the value of $T$ from part (a).

Calculate the cost of a school shirt ( $S$ ) using the cost of the short.