Solved on Jan 12, 2024

Find the total meal cost after an 18% tip on a $58 meal.
a) Let $m =$ meal cost. The equation is: $\text{Total Meal Cost} = m + 0.18m$
b) The total cost of the meal is = $\$68.44$

STEP 1

Assumptions
1. The cost of the meal before tax and tip is represented by $m$ .
2. The total cost of the meal including tax is $58$ dollars.
3. The tip is calculated as 18% of the meal cost before tax and tip.

STEP 2

To find the equation that represents the total cost of the meal including the tip, we need to express the tip as a percentage of the meal cost $m$ .
$Tip = m \times Tip\, rate$

STEP 3

Convert the tip percentage to a decimal value.
$18\% = 0.18$
$Tip = m \times 0.18$

STEP 4

The total meal cost including the tip can be represented as the sum of the meal cost $m$ and the tip.
$Total\, Meal\, Cost = m + Tip$

STEP 5

Substitute the expression for the tip from STEP_3 into the equation from STEP_4.
$Total\, Meal\, Cost = m + m \times 0.18$

STEP 6

Factor out $m$ from the right side of the equation to simplify.
$Total\, Meal\, Cost = m(1 + 0.18)$

STEP 7

Now we have the equation that represents the total meal cost including the tip.
$Total\, Meal\, Cost = m(1.18)$

STEP 8

Since we know the total meal cost including tax is $58$ dollars, we can set the equation from STEP_7 equal to $58$ .
$58 = m(1.18)$

STEP 9

To solve for $m$ , we need to divide both sides of the equation by $1.18$ .
$\frac{58}{1.18} = m$

STEP 10

Calculate the value of $m$ .
$m = \frac{58}{1.18}$

STEP 11

Perform the division to find the meal cost before tax and tip.
$m = \frac{58}{1.18} \approx 49.15$

STEP 12

Now that we have the meal cost before tax and tip, we can find the total cost of the meal including the tip by using the equation from STEP_7.
$Total\, Meal\, Cost = m(1.18)$

STEP 13

Plug in the value of $m$ into the equation.
$Total\, Meal\, Cost = 49.15(1.18)$

STEP 14

Calculate the total cost of the meal.
$Total\, Meal\, Cost = 49.15 \times 1.18 \approx 57.997$

STEP 15

Round the total cost to the nearest cent.
$Total\, Meal\, Cost \approx \$58.00$
The total cost of the meal, rounded to the nearest cent, is $58.00.

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Find the total meal cost after an 18% tip on a $58 meal.
a) Let $m =$ meal cost. The equation is: $\text{Total Meal Cost} = m + 0.18m$
b) The total cost of the meal is = $\$68.44$

STEP 1

Assumptions
1. The cost of the meal before tax and tip is represented by $m$ .
2. The total cost of the meal including tax is $58$ dollars.
3. The tip is calculated as 18% of the meal cost before tax and tip.

STEP 2

To find the equation that represents the total cost of the meal including the tip, we need to express the tip as a percentage of the meal cost $m$ .
$Tip = m \times Tip\, rate$

STEP 3

Convert the tip percentage to a decimal value.
$18\% = 0.18$
$Tip = m \times 0.18$

STEP 4

The total meal cost including the tip can be represented as the sum of the meal cost $m$ and the tip.
$Total\, Meal\, Cost = m + Tip$

STEP 5

Substitute the expression for the tip from STEP_3 into the equation from STEP_4.
$Total\, Meal\, Cost = m + m \times 0.18$

STEP 6

Factor out $m$ from the right side of the equation to simplify.
$Total\, Meal\, Cost = m(1 + 0.18)$

STEP 7

Now we have the equation that represents the total meal cost including the tip.
$Total\, Meal\, Cost = m(1.18)$

STEP 8

Since we know the total meal cost including tax is $58$ dollars, we can set the equation from STEP_7 equal to $58$ .
$58 = m(1.18)$

STEP 9

To solve for $m$ , we need to divide both sides of the equation by $1.18$ .
$\frac{58}{1.18} = m$

STEP 10

Calculate the value of $m$ .
$m = \frac{58}{1.18}$

STEP 11

Perform the division to find the meal cost before tax and tip.
$m = \frac{58}{1.18} \approx 49.15$

STEP 12

Now that we have the meal cost before tax and tip, we can find the total cost of the meal including the tip by using the equation from STEP_7.
$Total\, Meal\, Cost = m(1.18)$

STEP 13

Plug in the value of $m$ into the equation.
$Total\, Meal\, Cost = 49.15(1.18)$

STEP 14

Calculate the total cost of the meal.
$Total\, Meal\, Cost = 49.15 \times 1.18 \approx 57.997$

STEP 15

Round the total cost to the nearest cent.
$Total\, Meal\, Cost \approx \$58.00$
The total cost of the meal, rounded to the nearest cent, is $58.00.

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Find the total meal cost after an 18% tip on a $58 meal.a) Let m=m =m= meal cost. The equation is: Total Meal Cost=m+0.18m\text{Total Meal Cost} = m + 0.18mTotal Meal Cost=m+0.18mb) The total cost of the meal is = $68.44\$68.44$68.44

STEP 1

Assumptions1. The cost of the meal before tax and tip is represented by mmm.2. The total cost of the meal including tax is 585858 dollars.3. The tip is calculated as 18% of the meal cost before tax and tip.

STEP 2

To find the equation that represents the total cost of the meal including the tip, we need to express the tip as a percentage of the meal cost mmm.Tip=m×Tip rateTip = m \times Tip\, rateTip=m×Tiprate

STEP 3

Convert the tip percentage to a decimal value.18%=0.1818\% = 0.1818%=0.18Tip=m×0.18Tip = m \times 0.18Tip=m×0.18

STEP 4

The total meal cost including the tip can be represented as the sum of the meal cost mmm and the tip.Total Meal Cost=m+TipTotal\, Meal\, Cost = m + TipTotalMealCost=m+Tip

STEP 5

Substitute the expression for the tip from STEP_3 into the equation from STEP_4.Total Meal Cost=m+m×0.18Total\, Meal\, Cost = m + m \times 0.18TotalMealCost=m+m×0.18

STEP 6

Factor out mmm from the right side of the equation to simplify.Total Meal Cost=m(1+0.18)Total\, Meal\, Cost = m(1 + 0.18)TotalMealCost=m(1+0.18)

STEP 7

Now we have the equation that represents the total meal cost including the tip.Total Meal Cost=m(1.18)Total\, Meal\, Cost = m(1.18)TotalMealCost=m(1.18)

STEP 8

Since we know the total meal cost including tax is 585858 dollars, we can set the equation from STEP_7 equal to 585858.58=m(1.18)58 = m(1.18)58=m(1.18)

STEP 9

To solve for mmm, we need to divide both sides of the equation by 1.181.181.18.581.18=m\frac{58}{1.18} = m1.1858​=m

STEP 10

Calculate the value of mmm.m=581.18m = \frac{58}{1.18}m=1.1858​

STEP 11

Perform the division to find the meal cost before tax and tip.m=581.18≈49.15m = \frac{58}{1.18} \approx 49.15m=1.1858​≈49.15

STEP 12

Now that we have the meal cost before tax and tip, we can find the total cost of the meal including the tip by using the equation from STEP_7.Total Meal Cost=m(1.18)Total\, Meal\, Cost = m(1.18)TotalMealCost=m(1.18)

STEP 13

Plug in the value of mmm into the equation.Total Meal Cost=49.15(1.18)Total\, Meal\, Cost = 49.15(1.18)TotalMealCost=49.15(1.18)

STEP 14

Calculate the total cost of the meal.Total Meal Cost=49.15×1.18≈57.997Total\, Meal\, Cost = 49.15 \times 1.18 \approx 57.997TotalMealCost=49.15×1.18≈57.997

STEP 15

Round the total cost to the nearest cent.Total Meal Cost≈$58.00Total\, Meal\, Cost \approx \$58.00TotalMealCost≈$58.00The total cost of the meal, rounded to the nearest cent, is $58.00.

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Find the total meal cost after an 18% tip on a $58 meal.
a) Let $m =$ meal cost. The equation is: $\text{Total Meal Cost} = m + 0.18m$
b) The total cost of the meal is = $\$68.44$

Assumptions
1. The cost of the meal before tax and tip is represented by $m$ .
2. The total cost of the meal including tax is $58$ dollars.
3. The tip is calculated as 18% of the meal cost before tax and tip.

To find the equation that represents the total cost of the meal including the tip, we need to express the tip as a percentage of the meal cost $m$ .
$Tip = m \times Tip\, rate$

Convert the tip percentage to a decimal value.
$18\% = 0.18$
$Tip = m \times 0.18$

The total meal cost including the tip can be represented as the sum of the meal cost $m$ and the tip.
$Total\, Meal\, Cost = m + Tip$

Substitute the expression for the tip from STEP_3 into the equation from STEP_4.
$Total\, Meal\, Cost = m + m \times 0.18$

Factor out $m$ from the right side of the equation to simplify.
$Total\, Meal\, Cost = m(1 + 0.18)$

Now we have the equation that represents the total meal cost including the tip.
$Total\, Meal\, Cost = m(1.18)$

Since we know the total meal cost including tax is $58$ dollars, we can set the equation from STEP_7 equal to $58$ .
$58 = m(1.18)$

To solve for $m$ , we need to divide both sides of the equation by $1.18$ .
$\frac{58}{1.18} = m$

Calculate the value of $m$ .
$m = \frac{58}{1.18}$

Perform the division to find the meal cost before tax and tip.
$m = \frac{58}{1.18} \approx 49.15$

Now that we have the meal cost before tax and tip, we can find the total cost of the meal including the tip by using the equation from STEP_7.
$Total\, Meal\, Cost = m(1.18)$

Plug in the value of $m$ into the equation.
$Total\, Meal\, Cost = 49.15(1.18)$

Calculate the total cost of the meal.
$Total\, Meal\, Cost = 49.15 \times 1.18 \approx 57.997$

Round the total cost to the nearest cent.
$Total\, Meal\, Cost \approx \$58.00$
The total cost of the meal, rounded to the nearest cent, is $58.00.