A digital marketing firm runs advertisements on two platforms: SocialMedia and SearchEngin… — ACT

A digital marketing firm runs advertisements on two platforms: SocialMedia and SearchEngine. The cost to run an advertisement on SocialMedia is $15$ dollars per day, and the cost to run an advertisement on SearchEngine is $25$ dollars per day. Last month, the firm ran advertisements on both platforms for a combined total of $60$ days. The total amount spent on SocialMedia advertisements was $350$ dollars more than half the total amount spent on SearchEngine advertisements. For how many days last month did the firm run advertisements on SocialMedia?

Answer: 40 days

Answer

The firm ran advertisements on SocialMedia for 40 days.

Setting up the system of equations based on the problem description gives

S + E = 60

and

15S = 0.5(25E) + 350

. Substituting the first equation into the second yields

15S = 12.5(60 - S) + 350

. Solving this linear equation results in

S = 40

days.

Step-by-Step Solution

Define variables for the unknown quantities.

Let

S

be the number of days the firm ran advertisements on SocialMedia, and

E

be the number of days they ran advertisements on SearchEngine.

Establishing variables is the first step in translating a word problem into algebraic equations.

Express the relationship for the total number of days.

S + E = 60

, which simplifies to

E = 60 - S

This allows us to express one variable in terms of the other, making it easier to solve the system by substitution.

Translate the cost relationship statement into an algebraic equation.

15S = 12.5E + 350

The cost of running advertisements on SocialMedia is

15S

. The cost on SearchEngine is

25E

. Half of the SearchEngine cost is

12.5E

. Adding

350

to half of the SearchEngine cost gives the SocialMedia cost.

Substitute the expression for

E

into the cost equation and solve for

S

15S = 12.5(60 - S) + 350 \Rightarrow 15S = 750 - 12.5S + 350 \Rightarrow 27.5S = 1100 \Rightarrow S = 40

Solving the resulting linear equation yields the number of days spent on SocialMedia ads.

Key Concept

Translating and Solving Algebraic Word Problems

Estimated Time:2m 0s

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