Math / Algebra

QuestionQ10.
Kiaria is 7 years older than Jay. Martha is twice as old as Kiaria. The sum of their three ages is 77 Find the ratio of Jay's age to Kiaria's age to Martha's age.

Studdy Solution

STEP 1

1. Kiaria is 7 years older than Jay.
2. Martha is twice as old as Kiaria.
3. The sum of their three ages is 77.
4. We need to find the ratio of Jay's age to Kiaria's age to Martha's age.

STEP 2

1. Define variables for the ages of Jay, Kiaria, and Martha.
2. Write equations based on the problem statements.
3. Solve the system of equations to find the ages.
4. Calculate the ratio of their ages.

STEP 3

Define variables for the ages.
Let $j$ be Jay's age, $k$ be Kiaria's age, and $m$ be Martha's age.

STEP 4

Write equations based on the problem statements.
From the problem, we have:
1. Kiaria is 7 years older than Jay: $k = j + 7$
2. Martha is twice as old as Kiaria: $m = 2k$
3. The sum of their ages is 77: $j + k + m = 77$

STEP 5

Substitute the expressions for $k$ and $m$ into the sum equation.
Substitute $k = j + 7$ and $m = 2k$ into $j + k + m = 77$ :
$j + (j + 7) + 2(j + 7) = 77$
Simplify the equation:
$j + j + 7 + 2j + 14 = 77$
Combine like terms:
$4j + 21 = 77$

STEP 6

Solve for $j$ .
Subtract 21 from both sides:
$4j = 56$
Divide by 4:
$j = 14$

STEP 7

Find $k$ and $m$ using the values of $j$ .
Substitute $j = 14$ into $k = j + 7$ :
$k = 14 + 7 = 21$
Substitute $k = 21$ into $m = 2k$ :
$m = 2 \times 21 = 42$

STEP 8

Calculate the ratio of their ages.
The ratio of Jay's age to Kiaria's age to Martha's age is:
$j : k : m = 14 : 21 : 42$
Simplify the ratio by dividing each term by the greatest common divisor, which is 7:
$\frac{14}{7} : \frac{21}{7} : \frac{42}{7} = 2 : 3 : 6$
The ratio is:
$\boxed{2 : 3 : 6}$

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QuestionQ10.
Kiaria is 7 years older than Jay. Martha is twice as old as Kiaria. The sum of their three ages is 77 Find the ratio of Jay's age to Kiaria's age to Martha's age.

Studdy Solution

STEP 1

1. Kiaria is 7 years older than Jay.
2. Martha is twice as old as Kiaria.
3. The sum of their three ages is 77.
4. We need to find the ratio of Jay's age to Kiaria's age to Martha's age.

STEP 2

1. Define variables for the ages of Jay, Kiaria, and Martha.
2. Write equations based on the problem statements.
3. Solve the system of equations to find the ages.
4. Calculate the ratio of their ages.

STEP 3

Define variables for the ages.
Let $j$ be Jay's age, $k$ be Kiaria's age, and $m$ be Martha's age.

STEP 4

Write equations based on the problem statements.
From the problem, we have:
1. Kiaria is 7 years older than Jay: $k = j + 7$
2. Martha is twice as old as Kiaria: $m = 2k$
3. The sum of their ages is 77: $j + k + m = 77$

STEP 5

Substitute the expressions for $k$ and $m$ into the sum equation.
Substitute $k = j + 7$ and $m = 2k$ into $j + k + m = 77$ :
$j + (j + 7) + 2(j + 7) = 77$
Simplify the equation:
$j + j + 7 + 2j + 14 = 77$
Combine like terms:
$4j + 21 = 77$

STEP 6

Solve for $j$ .
Subtract 21 from both sides:
$4j = 56$
Divide by 4:
$j = 14$

STEP 7

Find $k$ and $m$ using the values of $j$ .
Substitute $j = 14$ into $k = j + 7$ :
$k = 14 + 7 = 21$
Substitute $k = 21$ into $m = 2k$ :
$m = 2 \times 21 = 42$

STEP 8

Calculate the ratio of their ages.
The ratio of Jay's age to Kiaria's age to Martha's age is:
$j : k : m = 14 : 21 : 42$
Simplify the ratio by dividing each term by the greatest common divisor, which is 7:
$\frac{14}{7} : \frac{21}{7} : \frac{42}{7} = 2 : 3 : 6$
The ratio is:
$\boxed{2 : 3 : 6}$

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QuestionQ10.Kiaria is 7 years older than Jay. Martha is twice as old as Kiaria. The sum of their three ages is 77 Find the ratio of Jay's age to Kiaria's age to Martha's age.

Studdy Solution

STEP 1

1. Kiaria is 7 years older than Jay.2. Martha is twice as old as Kiaria.3. The sum of their three ages is 77.4. We need to find the ratio of Jay's age to Kiaria's age to Martha's age.

STEP 2

1. Define variables for the ages of Jay, Kiaria, and Martha.2. Write equations based on the problem statements.3. Solve the system of equations to find the ages.4. Calculate the ratio of their ages.

STEP 3

Define variables for the ages.Let j j j be Jay's age, k k k be Kiaria's age, and m m m be Martha's age.

STEP 4

Write equations based on the problem statements.From the problem, we have:1. Kiaria is 7 years older than Jay: k=j+7 k = j + 7 k=j+72. Martha is twice as old as Kiaria: m=2k m = 2k m=2k3. The sum of their ages is 77: j+k+m=77 j + k + m = 77 j+k+m=77

STEP 5

STEP 6

Solve for j j j.Subtract 21 from both sides:4j=56 4j = 56 4j=56Divide by 4:j=14 j = 14 j=14

STEP 7

Find k k k and m m m using the values of j j j.Substitute j=14 j = 14 j=14 into k=j+7 k = j + 7 k=j+7:k=14+7=21 k = 14 + 7 = 21 k=14+7=21Substitute k=21 k = 21 k=21 into m=2k m = 2k m=2k:m=2×21=42 m = 2 \times 21 = 42 m=2×21=42

STEP 8

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QuestionQ10.
Kiaria is 7 years older than Jay. Martha is twice as old as Kiaria. The sum of their three ages is 77 Find the ratio of Jay's age to Kiaria's age to Martha's age.

1. Kiaria is 7 years older than Jay.
2. Martha is twice as old as Kiaria.
3. The sum of their three ages is 77.
4. We need to find the ratio of Jay's age to Kiaria's age to Martha's age.

1. Define variables for the ages of Jay, Kiaria, and Martha.
2. Write equations based on the problem statements.
3. Solve the system of equations to find the ages.
4. Calculate the ratio of their ages.

Define variables for the ages.
Let $j$ be Jay's age, $k$ be Kiaria's age, and $m$ be Martha's age.

Write equations based on the problem statements.
From the problem, we have:
1. Kiaria is 7 years older than Jay: $k = j + 7$
2. Martha is twice as old as Kiaria: $m = 2k$
3. The sum of their ages is 77: $j + k + m = 77$

Solve for $j$ .
Subtract 21 from both sides:
$4j = 56$
Divide by 4:
$j = 14$

Find $k$ and $m$ using the values of $j$ .
Substitute $j = 14$ into $k = j + 7$ :
$k = 14 + 7 = 21$
Substitute $k = 21$ into $m = 2k$ :
$m = 2 \times 21 = 42$