Question Keisha received a total of 115 phone calls over 3 evenings. The 3rd evening had 3 times the 2nd evening's calls. The 1st evening had 5 fewer calls than the 2nd evening. Find the number of calls per evening.

Studdy Solution

STEP 1

Assumptions
1. The total number of calls received over three evenings is 115.
2. The number of calls received on the third evening is three times the number received on the second evening.
3. The number of calls received on the first evening is five fewer than the number received on the second evening.

STEP 2

Let's denote the number of calls Keisha received on the second evening as $x$ . According to the problem, we can express the number of calls received on the first and third evenings in terms of $x$ .

STEP 3

The number of calls received on the first evening is $x - 5$ .

STEP 4

The number of calls received on the third evening is $3x$ .

STEP 5

Now we can set up an equation based on the total number of calls received over the three evenings.
$\text{Total calls} = \text{First evening} + \text{Second evening} + \text{Third evening}$

STEP 6

Substitute the expressions for the number of calls on each evening in terms of $x$ into the equation.
$115 = (x - 5) + x + 3x$

STEP 7

Combine like terms to simplify the equation.
$115 = 5x - 5$

STEP 8

Add 5 to both sides of the equation to isolate the terms with $x$ on one side.
$115 + 5 = 5x$

STEP 9

Simplify the left side of the equation.
$120 = 5x$

STEP 10

Divide both sides of the equation by 5 to solve for $x$ .
$\frac{120}{5} = x$

STEP 11

Calculate the value of $x$ .
$x = 24$

STEP 12

Now that we have the number of calls received on the second evening, we can find the number of calls received on the first and third evenings using the values of $x$ .

STEP 13

Substitute $x = 24$ into the expression for the first evening.
$\text{First evening} = x - 5$
$\text{First evening} = 24 - 5$

STEP 14

Calculate the number of calls received on the first evening.
$\text{First evening} = 19$

STEP 15

Substitute $x = 24$ into the expression for the third evening.
$\text{Third evening} = 3x$
$\text{Third evening} = 3 \times 24$

STEP 16

Calculate the number of calls received on the third evening.
$\text{Third evening} = 72$

STEP 17

We have now found the number of calls Keisha received each evening. On the first evening, she received 19 calls. On the second evening, she received 24 calls. On the third evening, she received 72 calls.
Keisha received 19 calls on the first evening, 24 calls on the second evening, and 72 calls on the third evening.

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Question Keisha received a total of 115 phone calls over 3 evenings. The 3rd evening had 3 times the 2nd evening's calls. The 1st evening had 5 fewer calls than the 2nd evening. Find the number of calls per evening.

Studdy Solution

STEP 1

STEP 2

Let's denote the number of calls Keisha received on the second evening as $x$ . According to the problem, we can express the number of calls received on the first and third evenings in terms of $x$ .

STEP 3

The number of calls received on the first evening is $x - 5$ .

STEP 4

The number of calls received on the third evening is $3x$ .

STEP 5

Now we can set up an equation based on the total number of calls received over the three evenings.
$\text{Total calls} = \text{First evening} + \text{Second evening} + \text{Third evening}$

STEP 6

Substitute the expressions for the number of calls on each evening in terms of $x$ into the equation.
$115 = (x - 5) + x + 3x$

STEP 7

Combine like terms to simplify the equation.
$115 = 5x - 5$

STEP 8

Add 5 to both sides of the equation to isolate the terms with $x$ on one side.
$115 + 5 = 5x$

STEP 9

Simplify the left side of the equation.
$120 = 5x$

STEP 10

Divide both sides of the equation by 5 to solve for $x$ .
$\frac{120}{5} = x$

STEP 11

Calculate the value of $x$ .
$x = 24$

STEP 12

Now that we have the number of calls received on the second evening, we can find the number of calls received on the first and third evenings using the values of $x$ .

STEP 13

Substitute $x = 24$ into the expression for the first evening.
$\text{First evening} = x - 5$
$\text{First evening} = 24 - 5$

STEP 14

Calculate the number of calls received on the first evening.
$\text{First evening} = 19$

STEP 15

Substitute $x = 24$ into the expression for the third evening.
$\text{Third evening} = 3x$
$\text{Third evening} = 3 \times 24$

STEP 16

Calculate the number of calls received on the third evening.
$\text{Third evening} = 72$

STEP 17

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Question Keisha received a total of 115 phone calls over 3 evenings. The 3rd evening had 3 times the 2nd evening's calls. The 1st evening had 5 fewer calls than the 2nd evening. Find the number of calls per evening.

Studdy Solution

STEP 1

STEP 2

Let's denote the number of calls Keisha received on the second evening as xxx. According to the problem, we can express the number of calls received on the first and third evenings in terms of xxx.

STEP 3

The number of calls received on the first evening is x−5x - 5x−5.

STEP 4

The number of calls received on the third evening is 3x3x3x.

STEP 5

Now we can set up an equation based on the total number of calls received over the three evenings.Total calls=First evening+Second evening+Third evening\text{Total calls} = \text{First evening} + \text{Second evening} + \text{Third evening}Total calls=First evening+Second evening+Third evening

STEP 6

Substitute the expressions for the number of calls on each evening in terms of xxx into the equation.115=(x−5)+x+3x115 = (x - 5) + x + 3x115=(x−5)+x+3x

STEP 7

Combine like terms to simplify the equation.115=5x−5115 = 5x - 5115=5x−5

STEP 8

Add 5 to both sides of the equation to isolate the terms with xxx on one side.115+5=5x115 + 5 = 5x115+5=5x

STEP 9

Simplify the left side of the equation.120=5x120 = 5x120=5x

STEP 10

Divide both sides of the equation by 5 to solve for xxx.1205=x\frac{120}{5} = x5120​=x

STEP 11

Calculate the value of xxx.x=24x = 24x=24

STEP 12

Now that we have the number of calls received on the second evening, we can find the number of calls received on the first and third evenings using the values of xxx.

STEP 13

Substitute x=24x = 24x=24 into the expression for the first evening.First evening=x−5\text{First evening} = x - 5First evening=x−5First evening=24−5\text{First evening} = 24 - 5First evening=24−5

STEP 14

Calculate the number of calls received on the first evening.First evening=19\text{First evening} = 19First evening=19

STEP 15

Substitute x=24x = 24x=24 into the expression for the third evening.Third evening=3x\text{Third evening} = 3xThird evening=3xThird evening=3×24\text{Third evening} = 3 \times 24Third evening=3×24

STEP 16

Calculate the number of calls received on the third evening.Third evening=72\text{Third evening} = 72Third evening=72

STEP 17

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Let's denote the number of calls Keisha received on the second evening as $x$ . According to the problem, we can express the number of calls received on the first and third evenings in terms of $x$ .

The number of calls received on the first evening is $x - 5$ .

The number of calls received on the third evening is $3x$ .

Now we can set up an equation based on the total number of calls received over the three evenings.
$\text{Total calls} = \text{First evening} + \text{Second evening} + \text{Third evening}$

Substitute the expressions for the number of calls on each evening in terms of $x$ into the equation.
$115 = (x - 5) + x + 3x$

Combine like terms to simplify the equation.
$115 = 5x - 5$

Add 5 to both sides of the equation to isolate the terms with $x$ on one side.
$115 + 5 = 5x$

Simplify the left side of the equation.
$120 = 5x$

Divide both sides of the equation by 5 to solve for $x$ .
$\frac{120}{5} = x$

Calculate the value of $x$ .
$x = 24$

Now that we have the number of calls received on the second evening, we can find the number of calls received on the first and third evenings using the values of $x$ .

Substitute $x = 24$ into the expression for the first evening.
$\text{First evening} = x - 5$
$\text{First evening} = 24 - 5$

Calculate the number of calls received on the first evening.
$\text{First evening} = 19$

Substitute $x = 24$ into the expression for the third evening.
$\text{Third evening} = 3x$
$\text{Third evening} = 3 \times 24$

Calculate the number of calls received on the third evening.
$\text{Third evening} = 72$