generals336

2021-09-12

solve each problem by setting up and solving an appropriate system of equations. Sue bought 3 packages of cookies and 2 sacks of potato chips for $13.50. Later she bought 2 more packages of cookies and 5 additional sacks of potato chips for$20.00. Find the price of a package of cookies.

sweererlirumeX

Consider the price of a package of cookies is x and the price of a sack of chips is y. The sum of 3 packages of cookies and 2 sacks of potato chips is $13.50, $3x+2y=13.50$, and the sum of 2 packages of cookies and 5 sacks of potato chips is$20, $2x+5y=20$.

Multiply $3x+2y=13.50$ by 2 and $2x+5y=20$ by 3 to get $6x+4y=27$ and $6x+15y=60$, respectively.

Subtract $6x+4y=27$ from $6x+15y=60$ to get $11y=33$.

$3x+2y=13.52x+5y=202\left(3x+2y=13.5\right)3\left(2x+5y=20\right)-\left(6x06+x11+514y=6-2037\right)3$

Divide both sides by 11 to obtain the price of a sack of chips, $3. Substitute y with 3 in $3x+2y=13.50$ to get $3x+6=13.50$. Subtract 6 from both sides and then divide by 3 to obtain the price of a package of cookies,$2.5 $3x+2y=13.503x+2\left(3\right)=13.503x=13.50-63x=7.5x=7.53=2.511y=33y=3311=3$

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