Question

practice 2

a. solve.

1. two houses are for sale on the same street. the second house has 1000 square feet less than twice the square feet of the first house. together the houses have 4400 square feet. what is the square footage of the first house?
2. julia has 24 coins in her pocket. the coins are either dimes or quarters. the total value of the coins is \\$4.50. how many coins are dimes? (hint: the value of the dimes is \\(0.10x\\), and the value of the quarters is \\(0.25(24-x)\\).)
3. the bulldogs won twice as many games as they lost. if they played a total of 36 games, how many did they win? (there were no tied games.)
4. the sum of four consecutive even numbers is 212. what is the third number? (hint: let \\(x =\\) the first number, \\(x + 2 =\\) the second number, \\(x + 4 =\\) the the third, and so on.)
5. a childrens store is selling pants for \\$6 each and shirts for \\$4. brenda bought 13 items and paid \\$62. how many shirts did she buy?
6. the sum of three consecutive numbers is 180. what is the least number in the series?
7. in a month andrew spends twice as much on rent as he does on food for his family. last month, he spent \\$1650 on rent and food. how much did he spend on rent?
8. george spends four times as much time helping customers as he does stocking shelves. last week, he spent 35 hours on the two tasks. how many hours were spent helping customers?

b. choose the one best answer to each question.

1. sylvia scored 10 points better than wiley on their science exam. greg scored 6 points less than wiley. altogether, the students earned 226 points. how many points did sylvia earn?

a. 74
b. 78
c. 84
d. 94

1. two adults and four children paid \\$48 to get into the fair. a childs ticket is \\$6 less than an adults ticket. what is the cost of an adults ticket?

a. \\$15
b. \\$12
c. \\$9
d. \\$6

1. jenny is four times as old as her niece tina. in 12 years, jenny will be only twice as old as tina. the chart shows expressions for tina and jennys ages now and in 12 years.

how old is tina now?
a. 4
b. 6
c. 8
d. 12

Explanation:

Step1: Solve Question 1

Let \(x\) be the first house's square footage:

$$x + (2x - 1000) = 4400 \implies 3x = 5400 \implies x = 1800$$

Step2: Solve Question 2

Let \(x\) be the number of dimes:

$$0.10x + 0.25(24 - x) = 4.50 \implies -0.15x = -1.50 \implies x = 10$$

Step3: Solve Question 3

Let \(w\) be wins and \(l\) be losses:

$$w = 2l, \quad w + l = 36 \implies 3l = 36 \implies l = 12, \quad w = 24$$

Step4: Solve Question 4

Let the four consecutive even numbers be \(x, x+2, x+4, x+6\):

$$4x + 12 = 212 \implies 4x = 200 \implies x = 50, \quad x+4 = 54$$

Step5: Solve Question 5

Let \(s\) be shirts and \(p\) be pants:

$$s + p = 13, \quad 4s + 6p = 62 \implies 4s + 6(13 - s) = 62 \implies s = 5$$

Step6: Solve Question 6

Let the three consecutive numbers be \(n, n+1, n+2\):

$$3n + 3 = 180 \implies 3n = 177 \implies n = 59$$

Step7: Solve Question 7

Let \(r\) be rent and \(f\) be food:

$$r = 2f, \quad r + f = 1650 \implies 3f = 1650 \implies f = 550, \quad r = 1100$$

Step8: Solve Question 8

Let \(h\) be helping and \(s\) be stocking:

$$h = 4s, \quad h + s = 35 \implies 5s = 35 \implies s = 7, \quad h = 28$$

Step9: Solve Question 9

Let Wiley's score be \(w\):

$$(w + 10) + w + (w - 6) = 226 \implies 3w = 222 \implies w = 74, \quad \text{Sylvia} = 84$$

Step10: Solve Question 10

Let adult ticket be \(a\) and child ticket be \(a - 6\):

$$2a + 4(a - 6) = 48 \implies 6a = 72 \implies a = 12$$

Step11: Solve Question 11

Set up the age equation in 12 years:

$$4x + 12 = 2(x + 12) \implies 2x = 12 \implies x = 6$$

Answer:

1. 1800 square feet
2. 10 dimes
3. 24 games
4. 54
5. 5 shirts
6. 59
7. \$1100
8. 28 hours
9. C. 84
10. B. \$12
11. B. 6