SOLUTION: 1.Danny is 9 years older than Harold. Together, their ages add up to 23. How old is Danny? 2. A triangle has two of its angles the same size. The other angle is 63� larger. What i

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Question 945313: 1.Danny is 9 years older than Harold. Together, their ages add up to 23. How old is Danny?
2. A triangle has two of its angles the same size. The other angle is 63� larger. What is the size of the largest angle?
3. A triangle has two of its angles the same size. The other angle is 72� larger. What is the size of one of the smaller angles?
4. Michael earns 3 times more than Becky in a week. In total, they earn $240 between them. How much did Michael earn?
Answer by macston(5194) (Show Source):
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1. AGES
D=Danny's age; H=Harold's age=D-9
D+H=23 Substitute for H
D+(D-9)=23 Add 9 to each side
2D=32 Divide each side by 2
D=16 ANSWER 1: Danny is 16 years old
D+H=23
16+H=23 Subtract 16 from each side
H=7 ANSWER 2: Harold is 7 years old
CHECK Danny is 9 years older (7+9=16) and sum is 23(16+7=23)
2. ANGLES(1) Let A=angles 1 and 2 and A+63 the third
Sum of angles in triangle=180 degrees:
A+A+A+63=180 degrees subtract 63 from each side
3A=117 degrees divide each side by 3
A=39 The smaller angles each measure 39 degrees
Larger angle=39+63=102 degrees ANSWER: The larger angle measures 102 degrees
3. ANGLES (2) Let A= angles 1 and 2 and A+72 degrees=the larger
Sum of angles in triangle=180 degrees
A+A+A+72=180 degrees Subtract 72 from each side
3A=108 degrees
A=36 degrees ANSWER The smaller angles each measure 36 degrees
4. EARNINGS Let B=Becky's earnings, M=Michael's earnings=3B
M+B=$240 Substitute for M
3B+B=240
4B=240
B=60 Becky earns $60 a week.
M=3B=3($60)=$180 ANSWER Michael earns $180 a week.
CHECK
M+B=$240
$180+$60=$240
$240=$240