QuestionOne number is 10 more than 16 times another. Their sum is 146. Find the numbers: $a, b$

Studdy Solution

STEP 1

Assumptions1. Let's denote the first number as $a$ and the second number as $b$ . . According to the problem, $a$ is10 more than sixteen times $b$ .
3. The sum of $a$ and $b$ is146.

STEP 2

First, we can write down the two equations according to the problem.
The first equation is from the statement "One number is10 more than sixteen times another":
$a =16b +10$ The second equation is from the statement "Their sum is146":
$a + b =146$

STEP 3

Now, we can substitute the first equation into the second equation to solve for $b$ .
Substitute $a =16b +10$ into $a + b =146$ $16b +10 + b =146$

STEP 4

Combine like terms $17b +10 =146$

STEP 5

Subtract10 from both sides of the equation to isolate the term with $b$ $17b =146 -10$

STEP 6

Calculate the right side of the equation $17b =136$

STEP 7

Divide both sides of the equation by17 to solve for $b$ $b = \frac{136}{17}$

STEP 8

Calculate the value of $b$ $b =8$

STEP 9

Now that we have the value of $b$ , we can substitute it into the first equation to solve for $a$ Substitute $b =8$ into $a =16b +$ $a =16 \cdot8 +$

STEP 10

Calculate the value of $a$ $a =128 +10 =138$ The numbers are138 and8.

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QuestionOne number is 10 more than 16 times another. Their sum is 146. Find the numbers: $a, b$

Studdy Solution

STEP 1

Assumptions1. Let's denote the first number as $a$ and the second number as $b$ . . According to the problem, $a$ is10 more than sixteen times $b$ .
3. The sum of $a$ and $b$ is146.

STEP 2

First, we can write down the two equations according to the problem.
The first equation is from the statement "One number is10 more than sixteen times another":
$a =16b +10$ The second equation is from the statement "Their sum is146":
$a + b =146$

STEP 3

Now, we can substitute the first equation into the second equation to solve for $b$ .
Substitute $a =16b +10$ into $a + b =146$ $16b +10 + b =146$

STEP 4

Combine like terms $17b +10 =146$

STEP 5

Subtract10 from both sides of the equation to isolate the term with $b$ $17b =146 -10$

STEP 6

Calculate the right side of the equation $17b =136$

STEP 7

Divide both sides of the equation by17 to solve for $b$ $b = \frac{136}{17}$

STEP 8

Calculate the value of $b$ $b =8$

STEP 9

Now that we have the value of $b$ , we can substitute it into the first equation to solve for $a$ Substitute $b =8$ into $a =16b +$ $a =16 \cdot8 +$

STEP 10

Calculate the value of $a$ $a =128 +10 =138$ The numbers are138 and8.

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QuestionOne number is 10 more than 16 times another. Their sum is 146. Find the numbers: a,ba, ba,b

Studdy Solution

STEP 1

Assumptions1. Let's denote the first number as aaa and the second number as bbb. . According to the problem, aaa is10 more than sixteen times bbb.3. The sum of aaa and bbb is146.

STEP 2

First, we can write down the two equations according to the problem.The first equation is from the statement "One number is10 more than sixteen times another":a=16b+10a =16b +10a=16b+10The second equation is from the statement "Their sum is146":a+b=146a + b =146a+b=146

STEP 3

Now, we can substitute the first equation into the second equation to solve for bbb.Substitute a=16b+10a =16b +10a=16b+10 into a+b=146a + b =146a+b=14616b+10+b=14616b +10 + b =14616b+10+b=146

STEP 4

Combine like terms17b+10=14617b +10 =14617b+10=146

STEP 5

Subtract10 from both sides of the equation to isolate the term with bbb17b=146−1017b =146 -1017b=146−10

STEP 6

Calculate the right side of the equation17b=13617b =13617b=136

STEP 7

Divide both sides of the equation by17 to solve for bbbb=13617b = \frac{136}{17}b=17136​

STEP 8

Calculate the value of bbbb=8b =8b=8

STEP 9

Now that we have the value of bbb, we can substitute it into the first equation to solve for aaaSubstitute b=8b =8b=8 into a=16b+a =16b +a=16b+a=16⋅8+a =16 \cdot8 +a=16⋅8+

STEP 10

Calculate the value of aaaa=128+10=138a =128 +10 =138a=128+10=138The numbers are138 and8.

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Studdy solves anything!

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

QuestionOne number is 10 more than 16 times another. Their sum is 146. Find the numbers: $a, b$

Assumptions1. Let's denote the first number as $a$ and the second number as $b$ . . According to the problem, $a$ is10 more than sixteen times $b$ .
3. The sum of $a$ and $b$ is146.

First, we can write down the two equations according to the problem.
The first equation is from the statement "One number is10 more than sixteen times another":
$a =16b +10$ The second equation is from the statement "Their sum is146":
$a + b =146$

Now, we can substitute the first equation into the second equation to solve for $b$ .
Substitute $a =16b +10$ into $a + b =146$ $16b +10 + b =146$

Combine like terms $17b +10 =146$

Subtract10 from both sides of the equation to isolate the term with $b$ $17b =146 -10$

Calculate the right side of the equation $17b =136$

Divide both sides of the equation by17 to solve for $b$ $b = \frac{136}{17}$

Calculate the value of $b$ $b =8$

Now that we have the value of $b$ , we can substitute it into the first equation to solve for $a$ Substitute $b =8$ into $a =16b +$ $a =16 \cdot8 +$

Calculate the value of $a$ $a =128 +10 =138$ The numbers are138 and8.