Sarah went to the grocery store and bought bottles of soda and bottles of juice. each
bottle of soda has 45 grams of sugar and each bottle of juice has 30 grams of sugar.
sarah purchased 5 more bottles of juice than bottles of soda and they all collectively
contain 525 grams of sugar. determine the number of bottles of soda purchased and
the number of bottles of juice purchased.

5 numbers of soda bottles and 10 numbers of juice bottle was purchased.

Step-by-step explanation:

Let Sarah purchased x bottles of Soda and y bottles of Juice.

Each soda bottle contains 45 gm of sugar and each juice bottle contains 30 gm of sugar, and there is a total of 525 gm of sugar,

Hence, we can write 45x + 30y = 525, ⇒ 3x + 2y = 35 (1)

Now, it is given that, she purchased 5 more bottles of juice than bottles of soda.

Hence, x + 5 = y, ⇒ x - y = - 5 (2)

Now, solving equations (1) and (2) we get, 5x = 25, ⇒ x = 5  

Hence,from equation (2), y = x + 5 = 10

Therefore, 5 numbers of soda bottles and 10 numbers of juice bottle was purchased. (Answer)