Grayson went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 35 grams of sugar and each bottle of juice has 15 grams of sugar. Grayson purchased 6 more bottles of soda than bottles of juice and they all collectively contain 410 grams of sugar. Determine the number of bottles of soda purchased and the number of bottles of juice purchased.

The number of bottles of soda purchased is 10 and the number of bottles of juice purchased is 4.

Step-by-step explanation:

Let us consider the soda bottles as x and juice bottles as y.

From the given data we can derive 2 equations,

35x+15y = 410 ... (1)

x=y+6 ... (2)

Substitute equation (2) in (1),

35 (y+6) + 15y=410.

35y + 210+15y=410.

50y+210=410.

50y=410-210.

50y=200.

y=4.

Substitute y value in equation (2),

x=4+6.

x=10.

The number of bottles of soda purchased is 10 and the number of bottles of juice purchased is 4.