Question

The number of bagels and coffee sold by a bagel shop yesterday can be modeled using the equation b+c=84. Their sales for the same day can be modeled using the equation 2b+c=145. Solve this system of equations using substitution. How many bagels and coffee were sold

Answer 1

Answer:

There were 61 bagels and 23 coffee sold

Step-by-step explanation:

Let us solve the question

∵ The number of bagels and coffee sold by a bagel shop yesterday

   can be modeled using the equation b + c = 84

∴ b + c = 84 ⇒ (1)

∵ Their sales for the same day can be modeled using the equation

   2b + c = 145

∴ 2b + c = 145 ⇒ (2)

Let us solve the system of equations using substitution

→ Subtract the two sides of equation (1) by b to find c in terms of b

∵ b - b + c = 84 - b

∴ c = 84 - b ⇒ (3)

→ Substitute c in equation (2) by equation (3)

∵ 2b + 84 - b = 145

→ Add the like terms on the left side

∴ (2b - b) + 84 = 145

∴ b + 84 = 145

→ Subtract 84 from both sides

∵ b + 84 - 84 = 145 - 84

∴ b = 61

→ Substitute the value of b in equation (3) to find c

∵ c = 84 - 61

∴ c = 23

∴ There were 61 bagels and 23 coffee sold.