On Monday, Luis picked up five scones and two large coffees for the office staff. He paid $17.63. On Tuesday, Rachel picked up four scones and seven large coffees for the office staff. She paid $24.85. What is the cost of one scone? What is the cost of one large coffee?
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5s + 2c = 17.63
4s + 7c = 24.85
Multiply first equation by 4 and second equation by -5, then add the equations together.
20s + 8c = 70.52
-20x - 35c = -124.25
-------------------------
-27c = -53.73
c = 1.99
a coffee costs $1.99
5s + 2·1.99 = 17.63
5s = 13.65
s = 2.73
a scone costs $2.73
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Let x is the cost of one scone and y is the cost of one large coffee. On Monday : the cost of 5 scones is 5x and the cost of two large coffee is 2 and the total he paid $17.63
We have the equation : 5 x + 2 y = 17.63. Similarly, the second equation : 4 x + 7 y = 24.85. Use the addition method, and eliminate x by multiplying the first equation and the second by 4 and 5 , respectively. 4 ( 5x + 2y = 17.63 ) => 20x + 8y = 70.52 :5( 4x + 7y = 24.85 ) => 20x + 35y = 124.25. Subtract the first equation from the second : 27 y = 53.73 => y = 1.99 then substitute the value of y into 5x + 2y = 17.63
=> x = 2.73. The cost of one scone $ 2.73 and the cost of one coffee $ 1.99