Question1. Acum doi ani, mama avea de 5 ori vârsta fiicei. În 6 ani, fiica va avea 1/3 din vârsta mamei. Poate mama avea 40 de ani? Determină vârsta fiicei.

Studdy Solution

STEP 1

Assumptions1. Vârsta mamei cu doi ani în urmă era de cinci ori mai mare decât vârsta fiicei. .este şase ani, vârsta fiicei va fi de trei ori mai mică decât vârsta mamei.
3. Trebuie să determinăm dacă vârsta mamei poate fi40 de ani în prezent și să determinăm vârsta actuală a fiicei.

STEP 2

Let's denote the mother's age two years ago as $M$ and the daughter's age two years ago as $. From the first condition, we have$ M =5$$

STEP 3

In six years, the mother's age will be $M +8$ and the daughter's age will be $+8$ . From the second condition, we have $+8 = \frac{1}{3}(M +8)$

STEP 4

We have a system of two equations with two variables $M$ and $$\begin{cases} M = \\ +8 = \frac{1}{3}(M +8) \end{cases}

STEP 5

We can solve this system of equations by substitution. Substitute $M =5$ into the second equation $+8 = \frac{1}{3}(5 +8)$

STEP 6

implify the equation $3 +24 =5 +8$

STEP 7

Rearrange the equation to solve for 2 =16$$

STEP 8

olve for =8$$

STEP 9

Substitute $=8$ into the first equation to find $M$ $M =5 \times8$

STEP 10

Calculate $M$ $M =40$

STEP 11

The mother's age two years ago was40, so her current age is42. Therefore, the mother's current age cannot be40.

STEP 12

The daughter's age two years ago was8, so her current age is10.
The mother's current age cannot be40, and the daughter's current age is10.

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Question1. Acum doi ani, mama avea de 5 ori vârsta fiicei. În 6 ani, fiica va avea 1/3 din vârsta mamei. Poate mama avea 40 de ani? Determină vârsta fiicei.

Studdy Solution

STEP 1

STEP 2

Let's denote the mother's age two years ago as $M$ and the daughter's age two years ago as $. From the first condition, we have$ M =5$$

STEP 3

In six years, the mother's age will be $M +8$ and the daughter's age will be $+8$ . From the second condition, we have $+8 = \frac{1}{3}(M +8)$

STEP 4

We have a system of two equations with two variables $M$ and $$\begin{cases} M = \\ +8 = \frac{1}{3}(M +8) \end{cases}

STEP 5

We can solve this system of equations by substitution. Substitute $M =5$ into the second equation $+8 = \frac{1}{3}(5 +8)$

STEP 6

implify the equation $3 +24 =5 +8$

STEP 7

Rearrange the equation to solve for 2 =16$$

STEP 8

olve for =8$$

STEP 9

Substitute $=8$ into the first equation to find $M$ $M =5 \times8$

STEP 10

Calculate $M$ $M =40$

STEP 11

The mother's age two years ago was40, so her current age is42. Therefore, the mother's current age cannot be40.

STEP 12

The daughter's age two years ago was8, so her current age is10.
The mother's current age cannot be40, and the daughter's current age is10.

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Question1. Acum doi ani, mama avea de 5 ori vârsta fiicei. În 6 ani, fiica va avea 1/3 din vârsta mamei. Poate mama avea 40 de ani? Determină vârsta fiicei.

Studdy Solution

STEP 1

STEP 2

Let's denote the mother's age two years ago as MMM and the daughter's age two years ago as .Fromthefirstcondition,wehave. From the first condition, we have.Fromthefirstcondition,wehaveM =5$$

STEP 3

In six years, the mother's age will be M+8M +8M+8 and the daughter's age will be +8 +8+8. From the second condition, we have+8=13(M+8) +8 = \frac{1}{3}(M +8)+8=31​(M+8)

STEP 4

We have a system of two equations with two variables MMM and $$\begin{cases} M = \\ +8 = \frac{1}{3}(M +8) \end{cases}

STEP 5

We can solve this system of equations by substitution. Substitute M=5M =5M=5 into the second equation+8=13(5+8) +8 = \frac{1}{3}(5 +8)+8=31​(5+8)

STEP 6

implify the equation3+24=5+83 +24 =5 +83+24=5+8

STEP 7

Rearrange the equation to solve for 2 =16$$

STEP 8

olve for =8$$

STEP 9

Substitute =8 =8=8 into the first equation to find MMMM=5×8M =5 \times8M=5×8

STEP 10

Calculate MMMM=40M =40M=40

STEP 11

The mother's age two years ago was40, so her current age is42. Therefore, the mother's current age cannot be40.

STEP 12

The daughter's age two years ago was8, so her current age is10.The mother's current age cannot be40, and the daughter's current age is10.

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Studdy solves anything!

Start learning now

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

Let's denote the mother's age two years ago as $M$ and the daughter's age two years ago as $. From the first condition, we have$ M =5$$

In six years, the mother's age will be $M +8$ and the daughter's age will be $+8$ . From the second condition, we have $+8 = \frac{1}{3}(M +8)$

We have a system of two equations with two variables $M$ and $$\begin{cases} M = \\ +8 = \frac{1}{3}(M +8) \end{cases}

We can solve this system of equations by substitution. Substitute $M =5$ into the second equation $+8 = \frac{1}{3}(5 +8)$

implify the equation $3 +24 =5 +8$

Substitute $=8$ into the first equation to find $M$ $M =5 \times8$

Calculate $M$ $M =40$

The daughter's age two years ago was8, so her current age is10.
The mother's current age cannot be40, and the daughter's current age is10.