Question

Caleb went to the grocery store and purchased cans of soup and frozen

dinners. Each can of soup has 200 mg of sodium and each frozen dinner has
500 mg of sodium. Caleb purchased a total of 15 cans of soup and frozen
dinners which collectively contain 4500 mg of sodium. Determine the
number of cans of soup purchased and the number of frozen dinners
purchased.

Answer 1

Caleb purchased 10 cans of soup and 5 frozen dinners.

Explanation:

Caleb purchased 10 cans of soup and 5 frozen dinners.

Let no. of can of soup be x and no. of frozen dinner be y.

To solve this, we can set up the following system of equations:

`\tt x + y = 15`......[i]

`\tt 200x + 500y = 4500`......[2]

Let's find the value by elimination method:

Multiplying equation one by 200.

we get,

`\tt 200 x+ 200 y = 15*200`

`\tt 200x +200 y =3000`

Subtracting equation 2 with equation 1.

`\tt (200x+500y)-(200x +200 y) =4500-3000`

`\tt \tt 300y = 1500`

`\tt y =(1500)/(300)`

`\tt y = 5`

Substitute the value of y into the first equation to find x.**

`\tt x + 5 = 15`

`\tt x = 15 - 5`

`\tt x = 10`

Therefore, Caleb purchased 10 cans of soup and 5 frozen dinners.

Answer 2

Cans of soup = 10

Frozen dinners = 5

Explanation:

To determine the number of cans of soup and frozen dinners Caleb purchased, set up and solve a system of equations based on the given information.

Let x be the number of cans of soup Caleb purchased.

Let y be the number of frozen dinners Caleb purchased.

Each can of soup has 200 mg of sodium and each frozen dinner has 500 mg of sodium. The total amount of sodium in the purchased cans and frozen dinners is 4500 mg. Therefore:

`200x + 500y = 4500`

Caleb purchased a total of 15 cans of soup and frozen dinners. Therefore:

`x + y = 15`

To solve the system of equations, rearrange the second equation to isolate x:

`\begin{aligned}x + y &= 15\\x + y -y&= 15-y\\x&=15-y\end{aligned}`

Substitute this into the first equation to eliminate the term in x, and solve for y:

`\begin{aligned}200(15-y) + 500y &= 4500\\3000-200y + 500y &= 4500\\3000+300y &= 4500\\3000+300y-3000 &= 4500-3000\\300y&=1500\\300y / 300&=1500 / 300\\y&=5\end{aligned}`

Therefore, Caleb purchased 5 frozen dinners.

Substitute the found value of y into the rearranged second equation and solve for x:

`\begin{aligned}x&=15-y\\x&=15-5\\x&=10\end{aligned}`

Therefore, Caleb purchased 10 cans of soup.