Today in class, Mr. Harbeck taught us how to do a problem solving question. Now, I'm going to scribe how to do/answer a problem solving question using numbers.
1. The second of two numbers is 4 times the first. Their sum is 50. Find the numbers.
The numbers are ____and____. (You can also write this at the end of the equation)
4x would be on the right side of the + sign, because it is the second number. The first number is x.
So, the equation would be like this:Let x = first #x + 4x = 50
5x = 50 (combined terms)
x = 10
The answer is 10, 40
You must write the formula x + 4x = 50
10 + 4(10) = 50
10 + 40 = 50
50 = 50
x = 10
4x = 40
2. The larger of two numbers is 12 more than the smaller. Their sum is 84. Find the numbers.
The numbers are ____,____,and ____. (You can also write this at the end of the equation)
Two other # would equal x because we don't know anything about them.
let x = small # 1 and small # 2
Two other # would equal x because we don't know anything about them.
let x = small # 1 and small # 2
x + 12 + x + x = 84
3x + 12 = 84 (combined terms)
-12 -123x = 72
x= 24
The answer is 36, 24, 24
3x + 12 = 84 (combined terms)
-12 -123x = 72
x= 24
The answer is 36, 24, 24
4. The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers.
The numbers are ____,and ____. (You can also write this at the end of the equation)
let x = first#
The numbers are ____,and ____. (You can also write this at the end of the equation)
let x = first#
5 more than twice the first
2x + 5
the sum is 80
= 80
x + 2x + 5 = 80
3x + 5 = 80
- 5 -53
x = 75
3x = 25
2x+5 = 55
x = 25
The answer is 25, 55
6. Find two numbers whose sum is 92, if the first is 4 more than 7 times the second. Find the first number.
The numbers are ____,and ____. (You can also write this at the end of the equation)
let x = second #
(7x + 4) + x = 92
8x + 4 = 92 (combined terms)
- 4 -4
8x = 88
8x = 11
(7x + 4) + x = 92
8(11) + 4 = 92
88 + 4 = 92
92 = 92x
= 117
x + 4 = 81
The answer is 11, 92
8. Together, a necklace and a bracelet cost $192. Find the price of each if the necklace costs 3 times as much as the bracelet.
The price is____. (You can also write this at the end of the equation)
Let x = bracelet
3x = Necklace
3x + x = 19
24x = 192
4x = $48 ($48.00)
3x = 3
(48)= 144
x = 48
$144.00+$48.00
$192.00
The price of a bracelet is $48.00 and the necklace is $144.00.
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