In a shop, 3 sweets cost the same as 1 bar of chocolate. Michelle bought 6 sweets and 4 bars of chocolate for $162. Find the cost of 1 bar of chocolate.
Question
In a shop, 3 sweets cost the same as 1 bar of chocolate. Michelle bought 6 sweets and 4 bars of chocolate for $162. Find the cost of 1 bar of chocolate.
Solution
Sure, let's solve this step by step:
Step 1: Let's denote the cost of 1 sweet as 's' and the cost of 1 bar of chocolate as 'c'.
Step 2: From the problem, we know that 3 sweets cost the same as 1 bar of chocolate. So, we can write this as an equation: 3s = c.
Step 3: We also know that Michelle bought 6 sweets and 4 bars of chocolate for $162. This can be written as another equation: 6s + 4c = 162.
Step 4: Now we have a system of two equations, and we can solve it. Let's substitute the first equation (3s = c) into the second one: 6s + 4(3s) = 162.
Step 5: Simplify the equation: 6s + 12s = 162.
Step 6: Combine like terms: 18s = 162.
Step 7: Solve for 's': s = 162 / 18 = 9.
Step 8: Now, let's find the cost of 1 bar of chocolate. Substitute 's' into the first equation: 3s = c, so c = 3 * 9 = $27.
So, 1 bar of chocolate costs $27.
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