Julian went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 25 grams of sugar and each bottle of juice has 40 grams of sugar. Julian purchased a total of 13 bottles of juice and soda which collectively contain 475 grams of sugar. Determine the number of bottles of soda purchased and the number of bottles of juice purchased

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absor201 absor201 · Answer 1 · 2020-02-08T17:33:34+01:00

3 bottles of soda and 10 bottles of juice were purchased.

Step-by-step explanation:

Given,

Sugar in each soda bottle = 25 grams

Sugar in each bottle of juice = 40 grams

Number of bottles purchased = 13

Sugar in 13 bottles = 475 grams

Let,

x be the number of soda bottles purchased

y be the number of juice bottles purchased

According to given statement;

x+y=13 Eqn 1

25x+40y=475 Eqn 2

Multiplying Eqn 1 by 25

[tex]25(x+y=13)\\25x+25y=325\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](25x+40y)-(25x+25y)=475-325\\25x+40y-25x-25y=150\\15y=150[/tex]

Dividing both sides by 15

[tex]\frac{15y}{15}=\frac{150}{15}\\y=10[/tex]

Putting y=10 in Eqn 1

[tex]x+10=13\\x=13-10\\x=3[/tex]

3 bottles of soda and 10 bottles of juice were purchased.

Keywords: linear equation, elimination method

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