Problem Solving

VJesus12 wrote: ↑

Thu Nov 05, 2020 8:19 am

At Joe's candy store, the total cost of \(1\) gumball and \(1\) lollipop is \(\$0.74.\) The total cost of \(1\) chocolate bar and \(1\) lollipop is \(\$0.92.\) The total cost of \(1\) gumball and \(1\) chocolate bar is \(\$1.24.\) What is the cost in dollars of \(1\) chocolate bar?

A. 0.53
B. 0.59
C. 0.63
D. 0.67
E. 0.71

Answer: E

Solution:

Let G, L and C be the cost of 1 gumball, 1 lollipop and 1 chocolate bar, respectively. We can create the equations:

G + L = 0.74

C + L = 0.92

and

G + C = 1.24

Adding the 3 equations together, we have:

2G + 2L + 2C = 2.9

G + L + C = 1.45

Since G + L = 0.74, we have


0.74 + C = 1.45

C = 0.71

Answer: E

VJesus12 wrote: ↑

Thu Nov 05, 2020 8:19 am

At Joe's candy store, the total cost of \(1\) gumball and \(1\) lollipop is \(\$0.74.\) The total cost of \(1\) chocolate bar and \(1\) lollipop is \(\$0.92.\) The total cost of \(1\) gumball and \(1\) chocolate bar is \(\$1.24.\) What is the cost in dollars of \(1\) chocolate bar?

A. 0.53
B. 0.59
C. 0.63
D. 0.67
E. 0.71

Answer: E

Source: Magoosh

We can solve this question using three variables or one variable.
Let's use one variable.

We're asked to find the cost of one chocolate bar.
So, let's let c = the cost of one chocolate bar (in dollars)

The total cost of 1 chocolate bar and 1 lollipop is $0.92.
So, the cost of 1 lollipop = $0.92 - (the cost of 1 chocolate bar)
In other words, the cost of 1 lollipop = 0.92 - c

The total cost of 1 gumball and 1 lollipop is $0.74.
So, the cost of 1 gumball = $0.74 - (the cost of 1 lollipop )
In other words, the cost of 1 gumball = 0.74 - (0.92 - c)
Simplify to get: the cost of 1 gumball = c - 0.18

The total cost of 1 gumball and 1 chocolate bar is $1.24
We can write: (c - 0.18) + (c) = 1.24
Simplify: 2c - 0.18 = 1.24
Add 0.18 to both sides: 2c = 1.42
Solve: c = 1.42/2 = 0.71

Answer: E