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At a bargain store, Spongebob bought 3 items that each cost the same amount. Patrick bought 5 items that each cost the same amount, but each was $1.50 less than the items that Spongebob bought. Both Spongebob and Patrick paid the same amount of money. What was the individual cost of each person's items?

Write an equation. Let x represent the cost of one of Spongebob's items.

Solve the equation. Show your work.

Check your solution. Show your work.

State the solution in complete sentences.

Respuesta :

Answer:

Cost of each item bought by Spongebob [tex]=x=\$3.75[/tex]

Cost of items bought by Spongebob = [tex]3x=3(3.75)=\$11.25[/tex]

Cost of each item bought by Patrick [tex]=x-1.50=3.75-1.50=\$2.25[/tex]

Cost of items bought by Patrick = [tex]5(x-1.50)=5(3.75-1.50)=\$11.25[/tex]

Step-by-step explanation:

Let [tex]x[/tex] denotes cost of each item bought by Spongebob.

Number of items bought by Spongebob = 3

So,

Cost of items bought by Spongebob = [tex]3x[/tex]

Cost of each item bought by Patrick = [tex]x-1.50[/tex]

Number of items bought by Patrick = 5

Cost of items bought by Patrick = [tex]5(x-1.50)[/tex]

Both Spongebob and Patrick paid the same amount of money.

So,

[tex]3x=5(x-1.50)\\3x=5x-7.5\\5x-3x=7.5\\2x=7.5\\x=\frac{7.5}{2} \\x=3.75[/tex]

So,

Cost of each item bought by Spongebob [tex]=x=\$3.75[/tex]

Cost of items bought by Spongebob = [tex]3x=3(3.75)=\$11.25[/tex]

Cost of each item bought by Patrick [tex]=x-1.50=3.75-1.50=\$2.25[/tex]

Cost of items bought by Patrick = [tex]5(x-1.50)=5(3.75-1.50)=\$11.25[/tex]