QuestionA boutique owner mixes 18 ounces of salt scrub costing \ $3.40 per ounce. How many ounces of tropical oil ($ \ $7.95$ ) and sea salt ( $\$ 1.45$ ) are needed?

Studdy Solution

STEP 1

Assumptions1. The total batch size is18 ounces. . The total cost per ounce of the batch is $3.40.<br />3. The cost per ounce of the tropical oil blend is$ 7.95.
4. The cost per ounce of the sea salt is $1.45.
5. The total cost of the batch is the sum of the costs of the tropical oil blend and the sea salt.

STEP 2

Let's denote the amount of tropical oil blend as $x$ ounces and the amount of sea salt as $y$ ounces. We can write down two equations based on the problem statement. The first equation is based on the total amount of the batch $x + y =18$

STEP 3

The second equation is based on the total cost of the batch. The total cost of the batch is the sum of the cost of the tropical oil blend and the cost of the sea salt, which should equal to the total cost per ounce times the total ounces $7.95x +1.45y =3.40 \\times18$

STEP 4

Now, we have a system of two equations with two variables. We can solve this system using substitution or elimination method. Let's use substitution method. First, solve the first equation for $x$ $x =18 - y$

STEP 5

Substitute $x$ from the first equation into the second equation $7.95(18 - y) +1.45y =3.40 \\times18$

STEP 6

implify the equation $142.65 -.95y +1.45y =61.2$

STEP 7

Combine like terms $142.65 -6.5y =61.2$

STEP 8

Subtract142.65 from both sides of the equation $-6.5y =61.2 -142.65$

STEP 9

Calculate the right side of the equation $-6.5y = -81.45$

STEP 10

Divide both sides of the equation by -6.5 to solve for $y$ $y = -81.45 / -6.5$

STEP 11

Calculate the value of $y$ $y =.5$

STEP 12

Now that we have the value for $y$ , we can substitute it into the first equation to solve for $x$ $x =18 -12.5$

STEP 13

Calculate the value of $x$ $x =5.5$ The boutique owner should use5.5 ounces of tropical oil blend and12.5 ounces of sea salt to make the18-ounce batch of her custom salt scrub.

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QuestionA boutique owner mixes 18 ounces of salt scrub costing \ $3.40 per ounce. How many ounces of tropical oil ($ \ $7.95$ ) and sea salt ( $\$ 1.45$ ) are needed?

Studdy Solution

STEP 1

STEP 2

Let's denote the amount of tropical oil blend as $x$ ounces and the amount of sea salt as $y$ ounces. We can write down two equations based on the problem statement. The first equation is based on the total amount of the batch $x + y =18$

STEP 3

The second equation is based on the total cost of the batch. The total cost of the batch is the sum of the cost of the tropical oil blend and the cost of the sea salt, which should equal to the total cost per ounce times the total ounces $7.95x +1.45y =3.40 \\times18$

STEP 4

Now, we have a system of two equations with two variables. We can solve this system using substitution or elimination method. Let's use substitution method. First, solve the first equation for $x$ $x =18 - y$

STEP 5

Substitute $x$ from the first equation into the second equation $7.95(18 - y) +1.45y =3.40 \\times18$

STEP 6

implify the equation $142.65 -.95y +1.45y =61.2$

STEP 7

Combine like terms $142.65 -6.5y =61.2$

STEP 8

Subtract142.65 from both sides of the equation $-6.5y =61.2 -142.65$

STEP 9

Calculate the right side of the equation $-6.5y = -81.45$

STEP 10

Divide both sides of the equation by -6.5 to solve for $y$ $y = -81.45 / -6.5$

STEP 11

Calculate the value of $y$ $y =.5$

STEP 12

Now that we have the value for $y$ , we can substitute it into the first equation to solve for $x$ $x =18 -12.5$

STEP 13

Calculate the value of $x$ $x =5.5$ The boutique owner should use5.5 ounces of tropical oil blend and12.5 ounces of sea salt to make the18-ounce batch of her custom salt scrub.

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QuestionA boutique owner mixes 18 ounces of salt scrub costing \3.40perounce.Howmanyouncesoftropicaloil(3.40 per ounce. How many ounces of tropical oil (3.40perounce.Howmanyouncesoftropicaloil(\7.95 7.957.95) and sea salt ($1.45\$ 1.45$1.45) are needed?

Studdy Solution

STEP 1

STEP 2

Let's denote the amount of tropical oil blend as xxx ounces and the amount of sea salt as yyy ounces. We can write down two equations based on the problem statement. The first equation is based on the total amount of the batchx+y=18x + y =18x+y=18

STEP 3

STEP 4

Now, we have a system of two equations with two variables. We can solve this system using substitution or elimination method. Let's use substitution method. First, solve the first equation for xxxx=18−yx =18 - yx=18−y

STEP 5

Substitute xxx from the first equation into the second equation7.95(18−y)+1.45y=3.40times187.95(18 - y) +1.45y =3.40 \\times187.95(18−y)+1.45y=3.40times18

STEP 6

implify the equation142.65−.95y+1.45y=61.2142.65 -.95y +1.45y =61.2142.65−.95y+1.45y=61.2

STEP 7

Combine like terms142.65−6.5y=61.2142.65 -6.5y =61.2142.65−6.5y=61.2

STEP 8

Subtract142.65 from both sides of the equation−6.5y=61.2−142.65-6.5y =61.2 -142.65−6.5y=61.2−142.65

STEP 9

Calculate the right side of the equation−6.5y=−81.45-6.5y = -81.45−6.5y=−81.45

STEP 10

Divide both sides of the equation by -6.5 to solve for yyyy=−81.45/−6.5y = -81.45 / -6.5y=−81.45/−6.5

STEP 11

Calculate the value of yyyy=.5y =.5y=.5

STEP 12

Now that we have the value for yyy, we can substitute it into the first equation to solve for xxxx=18−12.5x =18 -12.5x=18−12.5

STEP 13

Calculate the value of xxxx=5.5x =5.5x=5.5The boutique owner should use5.5 ounces of tropical oil blend and12.5 ounces of sea salt to make the18-ounce batch of her custom salt scrub.

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QuestionA boutique owner mixes 18 ounces of salt scrub costing \ $3.40 per ounce. How many ounces of tropical oil ($ \ $7.95$ ) and sea salt ( $\$ 1.45$ ) are needed?

Let's denote the amount of tropical oil blend as $x$ ounces and the amount of sea salt as $y$ ounces. We can write down two equations based on the problem statement. The first equation is based on the total amount of the batch $x + y =18$

Now, we have a system of two equations with two variables. We can solve this system using substitution or elimination method. Let's use substitution method. First, solve the first equation for $x$ $x =18 - y$

Substitute $x$ from the first equation into the second equation $7.95(18 - y) +1.45y =3.40 \\times18$

implify the equation $142.65 -.95y +1.45y =61.2$

Combine like terms $142.65 -6.5y =61.2$

Subtract142.65 from both sides of the equation $-6.5y =61.2 -142.65$

Calculate the right side of the equation $-6.5y = -81.45$

Divide both sides of the equation by -6.5 to solve for $y$ $y = -81.45 / -6.5$

Calculate the value of $y$ $y =.5$

Now that we have the value for $y$ , we can substitute it into the first equation to solve for $x$ $x =18 -12.5$

Calculate the value of $x$ $x =5.5$ The boutique owner should use5.5 ounces of tropical oil blend and12.5 ounces of sea salt to make the18-ounce batch of her custom salt scrub.