Question

mrs smith had 46$more than mrs wilson at first mrs wilson spent 4/7 of her money on some clothes and mrs smith spent 3/5 of her on household items after that they had an equal amount of money left find the total amount of money the two ladies spent.
please solve it as soon as posible

Answer 1

Using a system of equations, it is found that the total amount of money the two ladies spent was of $782.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

• Variable x: Amount Mrs. Smith had initially.

• Variable y: Amount Mrs. Wilson had initially.

Mrs smith had $46 more than Mr.s Wilson at first, hence:

x = y + 46.

Mrs Wilson spent 4/7 of her money on some clothes and, and Mrs. Smith spent 3/5 of her on household items, then they remained with an equal amount, so:

$\frac{2}{5}x = \frac{3}{7}y$

Since x = y + 46, we have that:

$\frac{2}{5}(y + 46) = \frac{3}{7}y$

14(y + 46) = 15y

y = 14 x 46

y = $644

x = 644 + 46 = $690

Hence the amount they spent is given as follows:

$\frac{3}{5}x + \frac{4}{7}y = \frac{3}{5} \times 690 + \frac{4}{7} \times 644 = 782$

More can be learned about a system of equations at https://brainly.com/question/24342899

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