Question

Divide 105 sweets amongst Thelma. Godfrey and Tina so that for every 2 sweets Thelma receives Godfrey receives 3 and for every 4 sweets Godfrey receives Tina receives 5. How many sweets did each receive?

Answer 1

Answer:

Godfrey  52.5

tina 21

thelma  35

Answer 2

Final Answer:

Among the 105 sweets, the number of sweets that Thelma. Godfrey and Tina individually receive, are 24, 36, and 45 respectively.

Given:

The 105 sweets are to be divided among Thelma. Godfrey and Tina such that for every 2 sweets Thelma receives Godfrey receives 3 sweets and for every 4 sweets Godfrey receives Tina receives 5 sweets. How many

To Find:

The number of sweets that Thelma. Godfrey and Tina individually receive are to be found.

Explanation:

The concept of ratios is important for the solution here.

The unitless ratio among the quantities measured with the same unit of measurement indicates their comparative presence with respect to each other.

Step 1 of 5

As per the statement given in the problem, assume the following.

• The number of sweets that Thelma individually receives is h.
• The number of sweets that Godfrey individually receives is g.
• The number of sweets that Tina individually receives is t.

Step 2 of 5

Using the information in the given problem, write the following ratios.

• $h:g=2:3$
• $g:t=4:5$

Step 3 of 5

In continuation with the above calculations, obtain these ratios in the following way.

• $h:g=2:3=(2\times 4):(3\times 4)=8:12$
• $g:t=4:5=(4\times 3):(5\times 3)=12:15$

• $h:g:t=8:12:15$

Step 4 of 5

Assuming k is the proportionality constant, write the following equations.

$\frac{h}{8} =\frac{g}{12} =\frac{t}{15} =k\\h=8k\\g=12k\\t=15k$

Step 5 of 5

From the above calculations, write and solve the following equation.

$8k+12k+15k=105\\35k=105\\k=\frac{105}{35} \\k=3$

Thus, the following is derived.

• The number of sweets that Thelma individually receives is

$h\\=8k\\=8\times 3\\=24$

• The number of sweets that Godfrey individually receives is

$g\\=12k\\=12\times 3\\=36$

• The number of sweets that Tina individually receives is

$t\\=15k\\=15\times 3\\=45$

Therefore, the required shares of Thelma. Godfrey and Tina are 24 sweets, 36 sweets, and 45 sweets respectively.

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