Question

Two apples and three peaches cost $1.65. three apples and two peaches cost $1.60. what is the cost of one peach

Answer 1

Let number of apples be a and peaches be p.
Number of apples = a
Number of peaches = p

Two apples and three peaches cost $1.65
⇒2a + 3p = 1.65

Three apples and two peaches cost $1.60
⇒3a + 2p = 1.60

System Equations :

`\begin{cases}&2a + 3p = 1.65 ---- (1) \\&3a + 2p = 1.60 ---- (2)\end{cases}`


`\begin{cases}&\text{Equation (1}) *3: 6a + 9p = 4.95 ---- (1a) \\&\text{Equation (2}) *2: 6a + 4p = 3.20 ---- (2a)\end{cases}`

Equation (1a) - (2a) :

`\begin{aligned} &5p = 1.75 \\&p = 0.35&\end{aligned}`

Answer: $0.35

Answer 2

Let a = cost of an apple and p = cost of a peach

From the two statements we can create the following system of equations:
2a + 3p = 1.65
3a + 2p = 1.60

Since we want to know the cost of a peach, let's eliminate the "a" terms by creating opposites. The LCM for 2 and 3 is 6 so I will multiply the top equation by 3 and the bottom equation by -2. This will create opposites to cancel "a" terms.
3(2a + 3p = 1.65) → 6a + 9p = 4.95
-2(3a + 2p = 1.60) → -6a - 4p = -3.20
The result of adding → 5p = 1.75
The result of ÷ 5 → p = .35
This means one peach cost .35 or 35 cents