SOLUTION: Ms. Shute ordered lunch for all the math teachers. The food was ordered from yummies and the choices were chicken sandwich meals for $3.63 or hamburger meals for $2.75. Michelle or
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Question 1170240: Ms. Shute ordered lunch for all the math teachers. The food was ordered from yummies and the choices were chicken sandwich meals for $3.63 or hamburger meals for $2.75. Michelle ordered a total of 15 meals. The ticket was $50.05. How many chicken sandwich meals were purchased? Found 2 solutions by josgarithmetic, greenestamps:Answer by josgarithmetic(39628) (Show Source):
You can of course practice using formal algebra to solve problems to get the answer to the problem. And since this problem is presumably from a course in basic algebra, you should understand how to set up and solve the problem that way.
But part of the purpose of studying mathematics is to develop problem solving skills in general.
You can get some good practice at that by solving this problem with logical reasoning and a bit of mental arithmetic.
Here is a quick solution without formal algebra.
(1) The average cost is about $50/15 = $10/3, or about $3.33; that is closer to $3.63 than it is to $2.75. So more chicken sandwich meals than hamburger meals were ordered.
(2) The total cost was $50.05, which is a multiple of 5 cents. The cost of each hamburger meal, $2.75, was also a multiple of 5 cents; so the total cost of the hamburger meals was a multiple of 5.
That means the total cost of the chicken sandwich meals must be a multiple of 5; and since the cost of each one is $3.63, the number of chicken sandwich meals must be a multiple of 5.
Putting (1) and (2) together, with a total of 15 meals being ordered, the answer has to be 10 chicken sandwich meals and 5 hamburger meals.
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