Question

Ali and Beth divide $$\mathrm{\$}280$$ in the ratio $$2:5$$. How much does each person get?

Answer 1

Hint: In order to find the solution of this question that is to divide $$\mathrm{\$}280$$ in the ratio $$2:5$$, first determine the total ratio or sum of total parts where ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent. After that calculate the value of one part then with the help of this value calculate the amount Ali and Beth will get.

Complete step-by-step solution:
According to the question, the given amount which needs to be divided between Ali and Beth is $$\mathrm{\$}280$$.
The ratio in which they are dividing the amount of $$\mathrm{\$}280$$ is $$2:5$$.
Here ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
To find out how much each person gets, we can interpret the total ratio into the parts given amount that is going to be divided. That is according to the question, the given ratio is $$2:5$$.
Therefore total no. of parts or total ratio is equal to $$2+5=7$$
Hence there are total $$7$$ parts.
Now we’ll evaluate the amount of one part that is:
$$\Rightarrow {\displaystyle \frac{280}{7}}=40$$
Therefore, value of one part is $$40\mathrm{\$}$$
According to the question, it’s clearly mentioned that Ali gets two parts out of seven. Amount Ali gets is:
$$\Rightarrow 40\mathrm{\$}\times 2$$ $$\text{parts}$$
$$\Rightarrow \text{80 }\mathrm{\$}$$
Hence, Ali will get $$\text{80 }\mathrm{\$}$$ out of $$\mathrm{\$}280$$.
According to the question, it’s clearly mentioned that Beth gets five parts out of seven. The amount Beth gets is :
$$\Rightarrow 40\mathrm{\$}\times 5$$ $$\text{parts}$$
$$\Rightarrow 20\text{0 }\mathrm{\$}$$
Hence, Beth will get $$20\text{0 }\mathrm{\$}$$ out of $$\mathrm{\$}280$$.
Therefore, Ali and Beth will get $$\text{80 }\mathrm{\$}$$ and $$20\text{0 }\mathrm{\$}$$ respectively.

Note: Students can go wrong by directly dividing the given ratio to the given amount. This is completely a wrong method which leads to the wrong answer. Key point is knowing the concept of ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.