1.The number of apples, a, is 6 less than half the number of pears, p.
Write an expression that represents the number of apples in terms of the number of pears.
2.Which equation can be used to solve the following word problem? Jason has 4 more nickels than dimes, and the total value of his coins is $2.75. How many nickels does he have? Let n represent the number of nickels. A) .10n + .05(n + 4) = 2.75 B) .10n – 4 + .05n = 2.75 C) .10(n + 4) + .05n = 2.75 D) .10(n-4) + .05n = 2.75
1) apples = pears/2 - 6
2) 0.05n + 0.1(n-4) = 2.75
1. To write an expression that represents the number of apples in terms of the number of pears, we can follow these steps:
Step 1: Determine what the problem is telling us about the relationship between the number of apples (a) and the number of pears (p). In this case, it says that the number of apples is 6 less than half the number of pears.
Step 2: Write down what we know in mathematical terms. We know that the number of apples (a) is 6 less than half the number of pears (p).
Step 3: Express this relationship in the form of an equation. Since "the number of apples (a) is 6 less than half the number of pears (p)", we can write the equation as: a = (1/2)p - 6.
Therefore, the expression that represents the number of apples in terms of the number of pears is: (1/2)p - 6.
2. To determine which equation can be used to solve the given word problem, we can go through the options and see which one accurately represents the problem.
The word problem states that Jason has 4 more nickels than dimes, and the total value of his coins is $2.75. Let n represent the number of nickels.
Let's examine each option and determine if it fits the given information:
Option A: .10n + .05(n + 4) = 2.75
Option B: .10n – 4 + .05n = 2.75
Option C: .10(n + 4) + .05n = 2.75
Option D: .10(n-4) + .05n = 2.75
Option A combines the value of nickels and dimes correctly, but it doesn't consider the fact that Jason has 4 more nickels than dimes. So, Option A is not the correct equation for this problem.
Option B incorrectly subtracts 4 from the value of dimes instead of nickels. It does mention adding the value of nickels to the value of dimes, but it doesn't account for the fact that Jason has 4 more nickels than dimes. So, Option B is also not the correct equation.
Option C considers the fact that Jason has 4 more nickels than dimes by adding 4 to the number of nickels (n + 4). It also adds the value of nickels and dimes correctly. So, Option C could potentially be the correct equation.
Option D mistakenly subtracts 4 from the number of nickels (n-4) instead of considering the fact that Jason has 4 more nickels than dimes. So, Option D is not the correct equation.
Therefore, the equation that can be used to solve the given word problem is Option C: .10(n + 4) + .05n = 2.75.