Question

Bonnie bought ten more cans of pop as she did bags of chips. She spent $17.50. Suppose a pop costs $1.00 and a bag of chips cost $0.50. How many of each item did Bonnie buy?​

Answer 1

SOLUTION: 5 bags of chips and 15 pops

Solving by substitution, choose your variables. In this case, let “c” represent the number of chips, and “p” the number of pop

Make your equations:

1.00p + 0.50c = 17.50

c + 10 = p

In the first equation, substitute “p” for the second equation:

1.00(c + 10) + 0.50c = 17.50

Distribute 1.00 to everything within the brackets:

1.00c + 10.00 + 0.50c = 17.50

Solve for “c”.

1.00c + 0.50c + 10.00 = 17.50

1.50c = 17.50 - 10.00

1.50c = 7.50

c = 5

Now, since we know that “p” is 10 more then “c”, we can substitute “c” for 5 in the second equation:

5 + 10 = p

15 = p

5 chips, 15 pops

Answer 2

Let
`x` be the number of bags of chips Bonnie bought.

Then, the number of cans of pop she bought is
`x + 10`.

The total cost is
`\$17.50`, so we can write an equation:

`\qquad\qquad 0.5x + 1(x + 10) = 17.50`

Simplifying and solving for x:

`\qquad\qquad\begin{gathered}0.5x + x + 10 = 17.50 \\ 1.5x + 10 = 17.50 \\ 1.5x = 7.50 \\ \fbox{x = 5}\end{gathered}`

`\therefore` Bonnie bought 5 bags of chips and 5 + 10 = 15 cans of pop.

To check:

• 
  `5` bags of chips cost
  `5 * \$0.50 = \$2.50`
• 
  `15` cans of pop cost
  `15 * \$1.00 = \$15.00`
• The total cost is
  `\$2.50 + \$15.00 = \bold{\$17.50}`.

`\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}`

(ノ^_^)ノ
`\large\qquad\qquad\qquad\rm 06/21/2023`