QuestionFind the father's age if the son is $\frac{1}{4}$ of his age and in 2 years, he is $\frac{7}{2}$ of the son's age.

Studdy Solution

STEP 1

Assumptions1. The son's current age is $\frac{1}{4}$ of the father's current age. . Two years from now, the father's age will be $\frac{7}{}$ times the son's age.
3. We are asked to find the father's current age.

STEP 2

Let's denote the father's current age as $and the son's current age as$ . According to the problem, we have $= \frac{1}{4}$

STEP 3

Two years from now, the father will be $+2$ years old and the son will be $+2$ years old. According to the problem, we have $+2 = \frac{7}{2}( +2)$

STEP 4

Now we have a system of two equations. We can solve this system to find the values of $and$ . Let's substitute $from the first equation into the second equation$ +2 = \frac{7}{2}\left(\frac{1}{4} +2\right)$$

STEP 5

implify the equation by multiplying through by2 to get rid of the fraction $2 +4 =7\left(\frac{1}{4} +2\right)$

STEP 6

istribute the on the right side of the equation $2 +4 = \frac{}{4} +14$

STEP 7

Multiply through by4 to get rid of the fraction $+16 =7 +56$

STEP 8

Rearrange the equation to isolate 8 -7 =56 -16$$

STEP 9

implify the equation $=40$ So, the father's current age is40 years.

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QuestionFind the father's age if the son is $\frac{1}{4}$ of his age and in 2 years, he is $\frac{7}{2}$ of the son's age.

Studdy Solution

STEP 1

Assumptions1. The son's current age is $\frac{1}{4}$ of the father's current age. . Two years from now, the father's age will be $\frac{7}{}$ times the son's age.
3. We are asked to find the father's current age.

STEP 2

Let's denote the father's current age as $and the son's current age as$ . According to the problem, we have $= \frac{1}{4}$

STEP 3

Two years from now, the father will be $+2$ years old and the son will be $+2$ years old. According to the problem, we have $+2 = \frac{7}{2}( +2)$

STEP 4

Now we have a system of two equations. We can solve this system to find the values of $and$ . Let's substitute $from the first equation into the second equation$ +2 = \frac{7}{2}\left(\frac{1}{4} +2\right)$$

STEP 5

implify the equation by multiplying through by2 to get rid of the fraction $2 +4 =7\left(\frac{1}{4} +2\right)$

STEP 6

istribute the on the right side of the equation $2 +4 = \frac{}{4} +14$

STEP 7

Multiply through by4 to get rid of the fraction $+16 =7 +56$

STEP 8

Rearrange the equation to isolate 8 -7 =56 -16$$

STEP 9

implify the equation $=40$ So, the father's current age is40 years.

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QuestionFind the father's age if the son is 14\frac{1}{4}41​ of his age and in 2 years, he is 72\frac{7}{2}27​ of the son's age.

Studdy Solution

STEP 1

Assumptions1. The son's current age is 14\frac{1}{4}41​ of the father's current age. . Two years from now, the father's age will be 7\frac{7}{}7​ times the son's age.3. We are asked to find the father's current age.

STEP 2

Let's denote the father's current age as andtheson′scurrentageas and the son's current age as andtheson′scurrentageas. According to the problem, we have=14 = \frac{1}{4}=41​

STEP 3

Two years from now, the father will be +2 +2+2 years old and the son will be +2 +2+2 years old. According to the problem, we have+2=72(+2) +2 = \frac{7}{2}( +2)+2=27​(+2)

STEP 4

Now we have a system of two equations. We can solve this system to find the values of and and and. Let's substitute fromthefirstequationintothesecondequation from the first equation into the second equationfromthefirstequationintothesecondequation +2 = \frac{7}{2}\left(\frac{1}{4} +2\right)$$

STEP 5

implify the equation by multiplying through by2 to get rid of the fraction2+4=7(14+2)2 +4 =7\left(\frac{1}{4} +2\right)2+4=7(41​+2)

STEP 6

istribute the on the right side of the equation2+4=4+142 +4 = \frac{}{4} +142+4=4​+14

STEP 7

Multiply through by4 to get rid of the fraction+16=7+56 +16 =7 +56+16=7+56

STEP 8

Rearrange the equation to isolate 8 -7 =56 -16$$

STEP 9

implify the equation=40 =40=40So, the father's current age is40 years.

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QuestionFind the father's age if the son is $\frac{1}{4}$ of his age and in 2 years, he is $\frac{7}{2}$ of the son's age.

Assumptions1. The son's current age is $\frac{1}{4}$ of the father's current age. . Two years from now, the father's age will be $\frac{7}{}$ times the son's age.
3. We are asked to find the father's current age.

Let's denote the father's current age as $and the son's current age as$ . According to the problem, we have $= \frac{1}{4}$

Two years from now, the father will be $+2$ years old and the son will be $+2$ years old. According to the problem, we have $+2 = \frac{7}{2}( +2)$

Now we have a system of two equations. We can solve this system to find the values of $and$ . Let's substitute $from the first equation into the second equation$ +2 = \frac{7}{2}\left(\frac{1}{4} +2\right)$$

implify the equation by multiplying through by2 to get rid of the fraction $2 +4 =7\left(\frac{1}{4} +2\right)$

istribute the on the right side of the equation $2 +4 = \frac{}{4} +14$

Multiply through by4 to get rid of the fraction $+16 =7 +56$

implify the equation $=40$ So, the father's current age is40 years.