Two varieties of pies are available at a fruit stand. Apple pies cost $5.75 each and cherry pies cost $6.50 each. Susan bought nine pies for a total cost of $53.25. There is no tax charged.
How many apple pies did Susan buy?
Set up a system of two equations. One equation will show the number of pies bought, and the other equation will involve the prices.
a = number of apple pies c = number of cherry pies a + c = 9 {Susan bought a total of nine pies} 5.75a + 6.5c = 53.25 {each apple pie costs $5.75 and each cherry pie costs $6.50} Use the substitution method by solving the first equation for a, and then substituting in. a + c = 9 {first equation} a = c + 9 {subtracted c from each side of first equation} Substitute (c + 9), in for a, into second equation} 5.75a + 6.5c = 53.25 {second equation} 5.75(c + 9) + 6.5c = 53.25 {substituted (c + 9) in for a into second equation} 5.75c + 51.75 + 6.5c = 53.25 {used distributive property} 0.75c + 51.75 = 53.25 {combined like terms} 0.75c = 1.5 {subtracted 51.75 from each side} c = 2 {divided each side by 0.75} Susan bought 2 cherry pies. Determine the number of apple pies by substituting 2, in for c, into the equation a = c + 9. a = c + 9 a = 2 + 9 {substituted 2 in for c} a = 7 {added} Susan bought 7 apple pies. Ask Algebra House
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