Jeff and Vincent went shopping together. Jeff spent £𝑎 and Vincent spent £𝑏. Vincent spent £55 more than Jeff. They spent £225 in total. What is the value of 𝑎?
Question
Jeff and Vincent went shopping together. Jeff spent £𝑎 and Vincent spent £𝑏. Vincent spent £55 more than Jeff. They spent £225 in total. What is the value of 𝑎?
Solution
Step 1: Understand the problem The problem is asking to find the amount of money that Jeff spent.
Step 2: Translate the problem into mathematical equations We know that Vincent spent £55 more than Jeff. This can be written as: b = a + 55
We also know that they spent £225 in total. This can be written as: a + b = 225
Step 3: Substitute the value of b from the first equation into the second equation Substituting b = a + 55 into the second equation gives: a + (a + 55) = 225
Step 4: Simplify the equation This simplifies to: 2a + 55 = 225
Step 5: Solve for a Subtract 55 from both sides of the equation to isolate 2a: 2a = 225 - 55 2a = 170
Then divide both sides by 2 to solve for a: a = 170 / 2 a = 85
So, Jeff spent £85.
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