Question

in 1-10, tell which given value, if any, is the solution of the equation.

1. $5.6 = l + 4.09$ $l = 0.7, 0.97, 1.51, 9.69$
2. $5k = 65$ $k = 11, 12, 13, 14$
3. $t - \\$5.60 = \\$1.04$ $t = \\$6.00, \\$6.10, \\$6.64, \\$7.00$
4. $133 \div y = 19$ $y = 6, 7, 8, 9$
5. $14 = \frac{u}{6}$ $u = 78, 81, 84, 90$
6. $9 + a = 46$ $a = 37, 39, 41, 55$
7. $6.8 = 2.89 + m$ $m = 3.9, 3.91, 4, 4.11$
8. $8c = 64$ $c = 6, 7, 8, 9$
9. $d \div 5.20 = 2.40$ $d = 10.92, 16.12, 17.68$
10. $m - 63.28 = 14.92$ $m = 77.0$ (partially visible)

Explanation:

Step1: Solve for \( l \) in \( 5.6 = l + 4.09 \)

Subtract \( 4.09 \) from both sides: \( l = 5.6 - 4.09 = 1.51 \)

Step2: Solve for \( k \) in \( 5k = 65 \)

Divide both sides by \( 5 \): \( k = \frac{65}{5} = 13 \)

Step3: Solve for \( t \) in \( t - 5.60 = 1.04 \)

Add \( 5.60 \) to both sides: \( t = 1.04 + 5.60 = 6.64 \)

Step4: Solve for \( y \) in \( 133 \div y = 19 \)

Rewrite as \( 19y = 133 \), then \( y = \frac{133}{19} = 7 \)

Step5: Solve for \( u \) in \( 14 = \frac{u}{6} \)

Multiply both sides by \( 6 \): \( u = 14 \times 6 = 84 \)

Step6: Solve for \( a \) in \( 9 + a = 46 \)

Subtract \( 9 \) from both sides: \( a = 46 - 9 = 37 \)

Step7: Solve for \( m \) in \( 6.8 = 2.89 + m \)

Subtract \( 2.89 \) from both sides: \( m = 6.8 - 2.89 = 3.91 \)

Step8: Solve for \( c \) in \( 8c = 64 \)

Divide both sides by \( 8 \): \( c = \frac{64}{8} = 8 \)

Step9: Solve for \( d \) in \( d \div 5.20 = 2.40 \)

Multiply both sides by \( 5.20 \): \( d = 2.40 \times 5.20 = 12.48 \)? Wait, no, recalculate: \( 2.4 \times 5.2 = (2 + 0.4)(5 + 0.2) = 10 + 0.4 + 2 + 0.08 = 12.48 \)? But the options are 10.92, 16.12, 17.68. Wait, maybe miscalculation. Wait, \( d = 2.40 \times 5.20 = 12.48 \), but the given options don't have 12.48? Wait, maybe the problem is \( d \div 5.20 = 2.40 \), so \( d = 2.40 \times 5.20 = 12.48 \), but the options are 10.92, 16.12, 17.68. Maybe a typo, but proceed. Wait, maybe I misread. Wait, the problem is \( d \div 5.20 = 2.40 \), so \( d = 2.4 \times 5.2 = 12.48 \), but the options are 10.92, 16.12, 17.68. Hmm. Maybe the original problem is different. Anyway, for the given options, maybe I made a mistake. Wait, no, let's check again. 5.20 * 2.40 = 12.48. So none? But the problem says "if any". Maybe the options are wrong, but proceed.

Step10: Solve for \( m \) in \( m - 63.28 = 14.92 \)

Add \( 63.28 \) to both sides: \( m = 14.92 + 63.28 = 78.2 \) (but the option is m=77.3? Wait, maybe the image has a typo, but assuming the problem is as is, \( m = 14.92 + 63.28 = 78.2 \))

Answer:

1. \( l = 1.51 \)
2. \( k = 13 \)
3. \( t = \$6.64 \)
4. \( y = 7 \)
5. \( u = 84 \)
6. \( a = 37 \)
7. \( m = 3.91 \)
8. \( c = 8 \)
9. No solution (or maybe typo, as \( d = 12.48 \) not in options)
10. \( m = 78.2 \) (assuming typo in option)