There were 90 cookies in a box. The number of raisin cookies was 2/3 the number of plain cookies. Chantalle ate an equal number of raisin and plain cookies. As a result, the ratio of the number of raisin cookies to the total number of cookies left was 1 : 5. How many cookies did Chantalle eat?

fractions, ratios

Let's assume the number of plain cookies is x.

According to the given information, the number of raisin cookies is 2/3 times the number of plain cookies. Therefore, the number of raisin cookies is (2/3)x.

Chantalle ate an equal number of raisin and plain cookies, so she ate x cookies from both types.

After Chantalle ate the cookies, the total number of cookies left is 90 - 2x (x plain cookies + x raisin cookies).

The ratio of the number of raisin cookies to the total number of cookies left is given as 1:5, which means (2/3)x : (90 - 2x) = 1:5.

To solve the equation, we can cross multiply:
5 * (2/3)x = 90 - 2x

Simplifying the equation:
10/3 x = 90 - 2x

Multiplying both sides by 3 to eliminate the denominator:
10x = 270 - 6x
16x = 270
x ≈ 16.875

Since the number of cookies can't be a decimal, we can round x to the nearest whole number which is 17.

Therefore, Chantalle ate 17 plain cookies and 17 raisin cookies. In total, she ate 34 cookies.

To solve this problem, let's break it down step by step:

Step 1: Let's assume the number of plain cookies is P.
According to the problem, the number of raisin cookies is 2/3 the number of plain cookies. So, the number of raisin cookies is (2/3)P.

Step 2: The total number of cookies is given as 90. So the equation becomes:
P + (2/3)P = 90
Combining like terms and solving for P:
(5/3)P = 90
P = (3/5) * 90
P = 54

Therefore, the number of plain cookies (P) is 54.

Step 3: It is mentioned that Chantalle ate an equal number of raisin and plain cookies. So, Chantalle ate 54 raisin cookies.

Step 4: The ratio of the number of raisin cookies to the total number of cookies left is given as 1:5. So, the total number of cookies left after Chantalle ate is 1/5 of the total. Let's assume the number of cookies Chantalle ate is C.

Therefore, (90 - C) = (1/5) * 90

Step 5: Solving for C:
90 - C = (1/5) * 90
90 - C = 18
C = 90 - 18
C = 72

Therefore, Chantalle ate 72 cookies.