QuestionAmir buys 3 cakes at $c$ cents each and 2 loaves at $(2c-11)$ cents. Total spent is \ $5.87. Find$ c$.

Studdy Solution

STEP 1

Assumptions1. Amir buys3 cakes that cost $c$ cents each. He also buys loaves of bread that cost $(c-11)$ cents each3. The total cost of his purchases is $\$5.87$ or $587$ cents

STEP 2

First, we need to set up an equation to represent the total cost of Amir's purchases. The total cost is the sum of the cost of the cakes and the cost of the bread.
$Total\, cost = Cost\, of\, cakes + Cost\, of\, bread$

STEP 3

Now, we can replace the cost of the cakes and the cost of the bread with the given expressions. The cost of the cakes is $3c$ (since there are3 cakes that cost $c$ cents each) and the cost of the bread is $2(2c-11)$ (since there are2 loaves of bread that cost $(2c-11)$ cents each).
$Total\, cost =3c +2(2c-11)$

STEP 4

We know that the total cost is $587$ cents, so we can set our equation equal to $587$ .
$3c +2(2c-11) =587$

STEP 5

Next, we need to simplify the equation. We can do this by distributing the $2$ in the term $2(2c-11)$ .
$3c +4c -22 =587$

STEP 6

Combine like terms on the left side of the equation.
$c -22 =587$

STEP 7

Add $22$ to both sides of the equation to isolate the term with $c$ on one side.
$7c =587 +22$

STEP 8

Calculate the right side of the equation.
$7c =609$

STEP 9

Finally, to find the value of $c$ , divide both sides of the equation by $7$ .
$c =609 /7$

STEP 10

Calculate the value of $c$ .
$c =87$ So, each cake costs $87$ cents.

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