Mathematics, 01.10.2019 22:20 missayers172

Gabriel 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 10 grams of sugar. gabriel purchased 2 more bottles of soda than bottles of juice and they all collectively contain 385 grams of sugar. determine the number of bottles of soda purchased and the number of bottles of juice purchased.

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Answer from: MannyRaw55

9 bottles of soda and 7 bottles of juice

Step-by-step explanation:

Let x be the number of bottles of soda purchased and y be the number of bottles of juice purchased.

1. Gabriel purchased 2 more bottles of soda than bottles of juice, then

x=y+2

2. Each bottle of soda has 35 grams of sugar, then there are 35x g of sugar in x bottles of soda.

Each bottle of juice has 10 grams of sugar, then there are 10y g of sugar in y bottles of juice.

In total, there are 35x+10y g of sugar.

All bottles collectively contain 385 grams of sugar, thus

35x+10y=385

3. Solve the system of two equations:

$\left\{\begin{array}{l}x=y+2\\ \\35x+10y=385\end{array}\right.$

Substitute the first equation into the second equation:

$35(y+2)+10y=385\\ \\35y+70+10y=385\\ \\35y+10y=385-70\\ \\45y=315\\ \\y=7\\ \\x=7+2=9$

Answer from: ladypink94

Gabriel bought 9 bottles of soda, and 7 bottles of sugar.

Step-by-step explanation:

This problem is solved by using a system of equations.

will be a bottle of soda, and will be a bottle of juice.

So, we know that each bottle of soda has 35 grams of sugar, this would expressed like: 35x .

In addition, each bottle of juice has 10 grams of sugar, this would be: 10y .

Now, the problem states that the total amount of sugar is 385 grams, this allows us to represent this with the equation:

35x+10y=385

The problem specifies that Gabriel purchased 2 more bottles of soda than juice, this is represents with this equation:

x=y+2

Now, we solve the system of equations 2x2, which will give us the result of each variable:

$\left \{ {{35x+10y=385} \atop {x=y+2}} \right.\\\left \{ {{35x+10y=385} \atop {(x-y=2})10} \right.\\\left \{ {{35x+10y=385} \atop (10x-10y=20}} \right.\\45x=405\\x=\frac{405}{45}=9$

This means that Gabriel purchased 9 bottles of soda.

Then, we replace this value in one of the equation to find the other result:

x=y+2

9=y+2

y=9-2

y=7

So, now we know that Gabriel bought 9 bottles of soda, and 7 bottles of sugar.

Answer from: Quest

step-by-step explanation:

each line from a vertex to the midpoint of the opposite side is called a median. the point where the medians intersect, point q, is the centroid.

the centroid of δabc is point q.

Lolol name the following segment or point. given: l, m, n are midpoints centroid of triangle abc p

Answer from: Quest

Answer is a not really sure tho

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