From a picture to an equation

The idea

An unknown quantity can be found by denoting it with a letter-number, expressing the given relationship as an equation, and solving that equation.

Eggs and bread slices

A scale balances 3 slices of bread, each weighing 2, against 2 fried eggs. Every egg weighs the same unknown amount, e.

Which equation says what the scale shows?

• 6 = e + e
• e + e = 2
• 6 + e = 2

Write the equation of the scale

For each scale: count the sacks (the unknown) and add up the loose weights on each pan. Write both sides, then find what one sack weighs.

Three moves: letter, equation, solve

1. Name the unknown with a letter-number. 2. Write what each pan weighs. The balance says the two are equal, so you get an equation. 3. Solve the equation to find the unknown.

The same works for stories that have no picture: if one plate of snacks costs ₹25 and delivery is a fixed ₹50, then *p* plates cost 25p + 50. If the total is ₹500, the equation is 25p + 50 = 500.

An unknown quantity can be found by denoting it with a letter-number, expressing the given relationship as an equation, and solving that equation.

• The scale shows | Equation | Solution
• 3 slices of 2 = 2 eggs | 6 = 2e | *e* = 3
• 16 = 4 and 2 sacks | 4 + 2y = 16 | *y* = 6
• 3 sacks and 5 = 20 | 3p + 5 = 20 | *p* = 5

Notes

To find an unknown: name it with a letter-number, write the relationship as an equation, then solve the equation. Here 4 + 2y = 16 gives *y* = 6.

Check yourself

Plates of snacks cost ₹25 each and delivery is a fixed ₹50. Madhubanti can spend ₹500 in all. With *p* plates, which equation says the total is exactly ₹500?

A scale has 2 sacks and a weight of 4 on the left pan and a weight of 16 on the right pan. Each sack weighs *y*. Which equation do you write?

From the scale, Sachin wrote 2e = 6 for two eggs of weight *e* against 6. What does one egg weigh?

Answer: 3

Two equal eggs weigh 6 together, so one weighs 6 ÷ 2 = 3. Check: 2 × 3 = 6.

A taxi charges a fixed ₹10 and then ₹8 for every km. A ride costs ₹58. With *k* km the cost is 8k + 10. Write 8k + 10 = 58 and find *k*.

Answer: 6

8 × 6 + 10 = 48 + 10 = 58, so k = 6 km.

• 25 + 50p = 500. This charges ₹50 for every plate. The ₹50 is paid only once, and ₹25 is the price of each plate.
• 25p + 50 = 500 — correct. Yes! The plates cost 25 × p, the delivery ₹50 is paid once, and the total is 500.
• 25p = 500 + 50. This adds the delivery to ₹500. Plates plus delivery make the total, so 25p + 50 = 500.
• 2 + 4y = 16. The 4 is a loose weight, not 4 sacks. The 2 is the number of sacks, so it goes with *y*.
• 6y = 16. This joins 2 sacks and a loose weight of 4 as if all were sacks. 2y and 4 are different kinds, so they cannot be joined.
• 2y + 4 = 16 — correct. Yes! Two sacks weigh 2y, the loose weight is 4, and the right pan weighs 16.