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.

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.