Question

taylor and emma sell hand - knit sweaters to raise money for charity. the tables show the total amount each person raises, y, as a function of the number of sweaters knitted, x. taylor’s sweaters sold, x: 0, 1, 2, 3, 4, 5, 6; amount raised ($), y: 0, 25, 50, 75, , , . emma’s sweaters sold, x: 0, 1, 2, 3, 4, 5, 6; amount raised ($), y: 0, 15, 30, 45, , , . each person hopes to raise $150. who do you think will reach the goal first? taylor emma

Explanation:

Step1: Find Taylor's rate

From the table, for Taylor, when \(x = 1\), \(y=25\). The rate (slope) \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1,25)\), \(m = 25\). The equation is \(y = 25x\). To find \(x\) when \(y = 150\), solve \(150=25x\), so \(x=\frac{150}{25}=6\).

Step2: Find Emma's rate

From the table, for Emma, when \(x = 1\), \(y = 15\). The rate (slope) \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1,15)\), \(m = 15\). The equation is \(y = 15x\). To find \(x\) when \(y = 150\), solve \(150=15x\), so \(x=\frac{150}{15}=10\).

Answer:

Taylor