To calculate: The calcium present in 1 cup of milk and in 1 cup of coo

vetrila10 2021-11-17 Answered
To calculate: The calcium present in 1 cup of milk and in 1 cup of cooked spinach if one day Shenika had 3 cups of milk and 1 cup of cooked spinach for a total of 1140 mg of calcium. The next day, she had 2 cups of milk and \(\displaystyle{1}{\frac{{{1}}}{{{2}}}}\) cups of cooked spinach for a total of 960 mg of calcium.

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Expert Answer

Coon2000
Answered 2021-11-18 Author has 8225 answers
Calculation:
Consider that Shenika had 3 cups of milk and 1 cup of cooked spinach for a total of 1140 mg of calcium. The next day, she had 2 cups of milk and \(\displaystyle{1}{\frac{{{1}}}{{{2}}}}\) cups of cooked spinach for a total of 960 mg of calcium.
Convert this problem into two system of equations.
Let the amount of calcium present in 1 cup of milk be x mg and the amount of calcium present in 1 cup of cooked spinach be y mg.
Shenika had 3 cups of milk and 1 cup of cooked spinach for a total of 1140 mg of calcium.
Now, this can be represented by a linear equation which is as follows,
\(\displaystyle{3}{x}+{y}={1140}\).....(1)
The next day, she had 2 cups of milk and \(\displaystyle{1}{\frac{{{1}}}{{{2}}}}\)cups of cooked spinach for a total of 960 mg of calcium.
Now, this can be represented by a linear equation which is as follows,
\(\displaystyle{2}{x}+{1.5}{y}={960}\)
Multiply with 10 to clear decimals of above equation.
\(\displaystyle{20}{x}+{15}{y}={9600}\)......(2)
\(\displaystyle{4}{x}+{3}{y}={1920}\)
So, the system of equation becomes as,
\(\displaystyle{3}{x}+{y}={1140}\)
\(\displaystyle{4}{x}+{3}{y}={1920}\)
Now, multiply the first equation with -3.
\(\displaystyle-{9}{x}-{3}{y}=-{3420}\)
\(\displaystyle{4}{x}+{3}{y}={1920}\)
Add these equations and solve for x.
\(\displaystyle-{9}{x}+{4}{x}-{3}{y}+{3}{y}=-{3420}+{1920}\)
\(\displaystyle—{5}{x}=-{1500}\)
\(\displaystyle{x}={\frac{{-{1500}}}{{-{5}}}}\)
\(\displaystyle{x}={300}\)
Substitute 300 for x in the (1) equation and solve for y.
\(\displaystyle{3}{\left({300}\right)}+{y}={1140}\)
\(\displaystyle{900}+{y}={1140}\)
\(\displaystyle{y}={1140}-{900}\)
\(\displaystyle{y}={240}\)
Substitute the ordered pair in each equation to verify the system of equation.
Substitute \(\displaystyle{\left({x},{y}\right)}={\left({300},{240}\right)}\) in first equation.
\(\displaystyle{3}\cdot{300}+{240}{\overset{{?}}{{=}}}{1140}\)
\(\displaystyle{900}+{240}{\overset{{?}}{{=}}}{1140}\)
\(\displaystyle{1140}={1140}\)
The result is true.
Substitute \(\displaystyle{\left({x},{y}\right)}={\left({300},{240}\right)}\) in second equation.
\(\displaystyle{4}\cdot{300}+{240}{\overset{{?}}{{=}}}{1920}\)
\(\displaystyle{1200}+{720}{\overset{{?}}{{=}}}{1920}\)
\(\displaystyle{1920}={1920}\)
The result is true.
Therefore, the calcium present in 1 cup of milk is 300 mg and in 1 cup of cooked spinach is 240 mg.
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