Respuesta :
10 oranges + 20 grapefruits = 35 pounds
16 oranges + 10 grapefruits = 23 pounds
13 oranges + 15 grapefruits = ?
Let x represent one orange and y represent one grapefruit, you can express the given equivalencies as equations:
10 oranges + 20 grapefruits = 35 pounds → 10x+20y=35
16 oranges + 10 grapefruits = 23 pounds→ 16x+10y=23
13 oranges + 15 grapefruits = ? → 13x+15y= ?
With this, we determined an equation system with two unknowns.
Write the first equation in terms of y:
[tex]\begin{gathered} 10x+20y=35 \\ 20y=35-10x \\ y=\frac{35}{20}-\frac{10}{20}x\text{ \rightarrow solve the divisions and simplify} \\ y=\frac{7}{4}-\frac{1}{2}x \end{gathered}[/tex]Next is to replace it in the second equation:
[tex]\begin{gathered} 16x+10y=23 \\ 16x+10(\frac{7}{4}-\frac{1}{2}x)=23 \\ 10x+10\cdot\frac{7}{4}+10\cdot(-\frac{1}{2}x)=23 \\ 10x+\frac{35}{2}-5x=23 \\ 10x-5x=23-\frac{35}{2} \\ 5x=\frac{11}{2} \\ x=\frac{11}{10} \end{gathered}[/tex]Third step is to calculate the value of y
[tex]\begin{gathered} y=\frac{7}{4}-\frac{1}{2}x \\ y=\frac{7}{4}-\frac{1}{2}\cdot\frac{11}{10} \\ y=\frac{6}{5} \end{gathered}[/tex]Finally, now that you know the values of x and y you can replace the third formula and calculate:
[tex]\begin{gathered} 13x+15y=\text{?} \\ 13\cdot\frac{11}{10}+15\cdot\frac{6}{5}=\frac{323}{10}=32.3 \end{gathered}[/tex]13 oranges and 15 grapefruits will weight 32.3 pounds
