Solved on Feb 02, 2024

Find the cost of a cake given that the cost of a cake is twice that of a cup of tea, and 1 cake and 5 cups of tea cost $£ 21$ .

STEP 1

Assumptions
1. The cost of a cake is twice the cost of a cup of tea.
2. The total cost of 1 cake and 5 cups of tea is £21.
Let's denote the cost of a cake as $C$ and the cost of a cup of tea as $T$ .

STEP 2

Express the cost of a cake in terms of the cost of a cup of tea.
$C = 2T$

STEP 3

Write an equation based on the given information about the total cost.
$1 \times C + 5 \times T = £21$

STEP 4

Substitute the expression for $C$ from STEP_2 into the equation from STEP_3.
$1 \times (2T) + 5 \times T = £21$

STEP 5

Simplify the equation by combining like terms.
$2T + 5T = £21$
$7T = £21$

STEP 6

Divide both sides of the equation by 7 to solve for $T$ .
$T = \frac{£21}{7}$

STEP 7

Calculate the cost of a cup of tea.
$T = £3$

STEP 8

Now that we have the cost of a cup of tea, we can find the cost of a cake using the expression from STEP_2.
$C = 2T$

STEP 9

Substitute the value of $T$ into the expression for $C$ .
$C = 2 \times £3$

STEP 10

Calculate the cost of a cake.
$C = £6$
The cost of a cake is £6.

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Find the cost of a cake given that the cost of a cake is twice that of a cup of tea, and 1 cake and 5 cups of tea cost $£ 21$ .

STEP 1

Assumptions
1. The cost of a cake is twice the cost of a cup of tea.
2. The total cost of 1 cake and 5 cups of tea is £21.
Let's denote the cost of a cake as $C$ and the cost of a cup of tea as $T$ .

STEP 2

Express the cost of a cake in terms of the cost of a cup of tea.
$C = 2T$

STEP 3

Write an equation based on the given information about the total cost.
$1 \times C + 5 \times T = £21$

STEP 4

Substitute the expression for $C$ from STEP_2 into the equation from STEP_3.
$1 \times (2T) + 5 \times T = £21$

STEP 5

Simplify the equation by combining like terms.
$2T + 5T = £21$
$7T = £21$

STEP 6

Divide both sides of the equation by 7 to solve for $T$ .
$T = \frac{£21}{7}$

STEP 7

Calculate the cost of a cup of tea.
$T = £3$

STEP 8

Now that we have the cost of a cup of tea, we can find the cost of a cake using the expression from STEP_2.
$C = 2T$

STEP 9

Substitute the value of $T$ into the expression for $C$ .
$C = 2 \times £3$

STEP 10

Calculate the cost of a cake.
$C = £6$
The cost of a cake is £6.

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Find the cost of a cake given that the cost of a cake is twice that of a cup of tea, and 1 cake and 5 cups of tea cost £21£ 21£21.

STEP 1

Assumptions1. The cost of a cake is twice the cost of a cup of tea.2. The total cost of 1 cake and 5 cups of tea is £21.Let's denote the cost of a cake as C C C and the cost of a cup of tea as T T T.

STEP 2

Express the cost of a cake in terms of the cost of a cup of tea.C=2T C = 2T C=2T

STEP 3

Write an equation based on the given information about the total cost.1×C+5×T=£21 1 \times C + 5 \times T = £21 1×C+5×T=£21

STEP 4

Substitute the expression for C C C from STEP_2 into the equation from STEP_3.1×(2T)+5×T=£21 1 \times (2T) + 5 \times T = £21 1×(2T)+5×T=£21

STEP 5

Simplify the equation by combining like terms.2T+5T=£21 2T + 5T = £21 2T+5T=£217T=£21 7T = £21 7T=£21

STEP 6

Divide both sides of the equation by 7 to solve for T T T.T=£217 T = \frac{£21}{7} T=7£21​

STEP 7

Calculate the cost of a cup of tea.T=£3 T = £3 T=£3

STEP 8

Now that we have the cost of a cup of tea, we can find the cost of a cake using the expression from STEP_2.C=2T C = 2T C=2T

STEP 9

Substitute the value of T T T into the expression for C C C.C=2×£3 C = 2 \times £3 C=2×£3

STEP 10

Calculate the cost of a cake.C=£6 C = £6 C=£6The cost of a cake is £6.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the cost of a cake given that the cost of a cake is twice that of a cup of tea, and 1 cake and 5 cups of tea cost $£ 21$ .

Assumptions
1. The cost of a cake is twice the cost of a cup of tea.
2. The total cost of 1 cake and 5 cups of tea is £21.
Let's denote the cost of a cake as $C$ and the cost of a cup of tea as $T$ .

Express the cost of a cake in terms of the cost of a cup of tea.
$C = 2T$

Write an equation based on the given information about the total cost.
$1 \times C + 5 \times T = £21$

Substitute the expression for $C$ from STEP_2 into the equation from STEP_3.
$1 \times (2T) + 5 \times T = £21$

Simplify the equation by combining like terms.
$2T + 5T = £21$
$7T = £21$

Divide both sides of the equation by 7 to solve for $T$ .
$T = \frac{£21}{7}$

Calculate the cost of a cup of tea.
$T = £3$

Now that we have the cost of a cup of tea, we can find the cost of a cake using the expression from STEP_2.
$C = 2T$

Substitute the value of $T$ into the expression for $C$ .
$C = 2 \times £3$

Calculate the cost of a cake.
$C = £6$
The cost of a cake is £6.