The sum of ages of a mother and daughter is 45 years. Five years ago, the product of their ages was four times the mother's age at that time. The present age of the mother is.?​

the answer is 36

Step-by-step explanation:

we can solve this using an algebra equation

so first from the world problem, we can tell that mother and daughter's ages added together is 45 we can represent this by saying x (mother's age), plus y (daughter's age) is 45.

(x+y)=45

Then we from the problem we know that 5 years ago the product of their ages is four times the mother's age at that time. From this, we can write

(x-5)*(y-5)=4*(x-5)

Then we just subtract the common denominators which is (x-5) so then the equation becomes

(y-5)=4

add 5 to both sides

y=9

Then all we do is plug the answer for y into the very first equation

x+9=45

Subtract both sides by 9

x=36

To double-check let's put the answers in the second equation

(36-5)*(9-5)=4*(x-5)

we get

(31)*(4)=4*(31)

so it's right I think

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places